SOLVING LINEAR INEQUALITIES


 Cornelius Boone
 1 years ago
 Views:
Transcription
1 Topic 15: Solving linear inequalities 65 SOLVING LINEAR INEQUALITIES Lesson 15.1 Inequalities on the number line 15.1 OPENER Consider the inequality x > List five numbers that make the inequality true. 2. Plot your five numbers on the number line. 3. Does an x value of 7.25 make the inequality true? 4. Does an x value of make the inequality true? 5. Write a sentence that describes all of the numbers that make this inequality true CORE ACTIVITY 1. Graph the solutions for the following mathematical statements: a. x = b. x <  4 c. x > 0 d. x >  7 e. x < f. x 5
2 66 Unit 5 Linear equations and inequalities 2. Consider this compound inequality: x < 1 or x > 4 a. Complete the table by determining whether the values for x make the statement true. Value for x Makes the statement true Yes/No π 7 12 b. List five additional numbers that make this compound inequality true. 3. a. Construct a graph on the number line to represent the inequality x < 1. b. Construct a graph on the number line to represent the inequality x > 4. c. Construct a graph on the number line to show ALL the numbers that make the compound inequality x < 1 or x > 4 true. Use the graphs you sketched in 3a and 3b to help you. 4. On a number line, show all of the numbers, x, such that x >  2 or x < 7.
3 Topic 15: Solving linear inequalities Consider the following compound inequality: x > 2 and x < 7 a. Complete the table by determining whether the values for x make the statement true. Value for x Makes the statement true Yes/No π 7 12 b. List five additional numbers that make this statement true. 6. a. Construct a graph on the number line to represent the inequality x > 2. b. Construct a graph on the number line to represent the inequality x < 7. c. Construct a graph on the number line to show ALL the numbers that make the statement in question 5 true. To help you construct the final graph, consider your work from questions 5a and 5b. 7. On a number line, show all of the numbers, x, such that x <  3 and x 2.
4 68 Unit 5 Linear equations and inequalities 8. Construct a graph on each number line to show the solution set for each compound inequality. Then, describe the solution set for each compound inequality using one of these four descriptions: (1) some but not all real numbers, (2) an empty set, (3) all real numbers, or (4) exactly one number. Graph a. x < 4 and x > 6 Solution set b. x < 6 or x > 4 c. x < 6 and x > 4 d. x < 4 or x > 6 e. x 5 or x 5 f. x 5 and x CONSOLIDATION ACTIVITY 1. For each card numbered 1 through 10, work with your partner to find a match using the lettered cards. Then, write the letter of the matching card in the table. Inequality card number Number line card letter 2. Write an equation or inequality that would produce the same number line graph as x 4 and x 4 3. Write an equation or inequality that would produce the same number line graph as x < 5 or x Write an equation or inequality that would produce the same number line graph as x < 4 or x > 4.
5 Topic 15: Solving linear inequalities 69 HOMEWORK 15.1 Notes or additional instructions based on whole class discussion of homework assignment: 1. Match the inequality to its representation on a number line. a. x < i. b. x ii. c. x > iii. d. x = iv. e. x < v. f. x > vi. 2. Write an inequality statement whose solution is an empty set. 3. Write an inequality statement whose solution is some but not all real numbers. Graph the solution on a number line. 4. Write an inequality statement whose solution is all real numbers. Graph the solution on a number line. 5. Write an inequality statement whose solution is exactly one number. Graph the solution on a number line. 6. Write an inequality statement to represent the graph shown. 7. Write an inequality statement to represent the graph shown.
6 70 Unit 5 Linear equations and inequalities STAYING SHARP 15.1 Practicing algebra skills & concepts 1. Select the appropriate symbol (<, >, or =) to describe the relationship between each pair of numbers. a b c List the lines according to the value of their slopes. List them in order from the smallest slope value to the largest slope value. d Which pair of x and y coordinates appears in the tables for both functions? Answer: 4. What are the coordinates of the point of intersection of the two lines in the graph? Preparing for upcoming lessons Answer: y = 2x 7 y = 3x Answer: Focus skill: Slope and geometric connections 5. What is the slope of the line? A slope triangle is drawn for you. Answer: 6. Write an equation for the line in Question 5. Answer with supporting work:
7 Topic 15: Solving linear inequalities 71 Lesson 15.2 Introduction to solving linear inequalities 15.2 OPENER A car rental company charges $29.95 plus 16 cents per mile for each mile driven. 1. Write a function rule to describe the relationship between the cost of the rental, r, and the number of miles you drove, m. 2. What input value would result in an output value of $75? 15.2 CORE ACTIVITY 1. Write an inequality to represent the situation below. A car rental company charges $29.95 plus 16 cents per mile for each mile driven. Your boss is very careful with the company's money. She wants you to plan your business trips so you will not spend more than $75 for car rental fees. 2. Solve the inequality you wrote in question 1 to determine how many miles you could drive and spend $75 or less for the trip. Your teacher will assign you and your partner a particular method for solving the inequality. Create a poster presenting your solution. 3. List the four methods you will be using in this topic to solve linear inequalities. 4. Complete a journal entry. Vocabulary term My understanding of what the term means An example that shows the meaning of the term Linear inequality
8 72 Unit 5 Linear equations and inequalities 15.2 CONSOLIDATION ACTIVITY Your boss is still trying to save money on car rentals. You compare Omega Car Rental, which charges $72.00 per day with unlimited free mileage, and Optimal Car Rental, which charges $22.90 plus 30 cents per mile. 1. Some days you drive many miles, and some days you drive fewer miles. Determine the range of daily mileage for which each company is the less expensive choice. 3. Write a report to your boss that includes your recommendations about which car rental company to use depending on the number of miles you plan to drive. Explain how you arrived at your recommendation. Use computations, graphs, or tables to provide support for your conclusions.
9 Topic 15: Solving linear inequalities 73 HOMEWORK 15.2 Notes or additional instructions based on whole class discussion of homework assignment: 1. Solve and graph the solutions to the inequalities below using any of the methods from class: a table, a graph, undoing, or algebraic operations. (You may need to use a separate sheet of notebook paper or graph paper.) a. x + 3 > 2 b. 15x 45 c. 3 < 4x  5 d. 2x e. 5 > x 1 f. 1.5x < The students on the dance committee at Jefferson High School are planning a dance. They hope to make a profit of at least $150 to donate to a local animal shelter. The dance committee has decided to sell tickets for $5. They also know that the cost for the DJ will be $200. a. The inequality 150 5x 200 can be used to determine if the dance committee met its goal. Explain how each part of this inequality fits the problem situation. b. Solve the inequality using a table, a graph, undoing, or algebraic operations. (You may need to use a separate sheet of graph paper.) c. d. In a complete sentence, explain what your solution to part b means in the context of the problem situation.
10 74 Unit 5 Linear equations and inequalities STAYING SHARP 15.2 Practicing algebra skills & concepts 1. Select the appropriate symbol (<, >, or =) to describe the relationship between each pair of numbers. a b c d On the coordinate plane, sketch a line that has an x intercept of ( 2,0) and a y intercept of (0,6). Then, calculate the slope of the line. e Slope of line: Preparing for upcoming lessons Complete these tables to answer questions 3 and 4. Table A Table B y = x + 4 y = 0.5x a. As x increases by 1, by how much does y change in Table A? b. As x increases by 1, by how much does y change in Table B? 4. Will there be a common (x,y) pair in the two tables if the tables are continued? Explain. Focus skill: Slope and geometric connections Use the two slope triangles to answer Questions 5 and a. Calculate the slope of the line using the smaller slope triangle. b. Calculate the slope of the line using the larger slope triangle. 6. Explain why the two slopes you calculated are equal.
11 Topic 15: Solving linear inequalities 75 Lesson 15.3 Solving inequalities using graphs and tables 15.3 OPENER Use your graphing calculator to solve the equation!3x!1 = 1 x + 6 using a table and graph. Sketch both the graph display 2 and the table display from your calculator screen CORE ACTIVITY Use the graph you created in the Opener to answer these questions: 1. For which values of x is the inequality!3x!1 < 1 2 x + 6 true? 2. For which values of x is the inequality!3x!1 > 1 2 x + 6 true? 3. How did solving the equation in the Opener help you answer questions 1 and 2? 4. Complete a journal entry explaining how to use each of the given methods to solve an inequality in one variable. Each explanation should include an example. Using table technology to solve inequalities Using graphing technology to solve inequalities 15.3 CONSOLIDATION ACTIVITY
12 76 Unit 5 Linear equations and inequalities 1. Solve the following inequalities using the table and graphing features on your graphing calculator. Sketch the calculator graph you used to solve the inequality. Also, copy the calculator table that you used. State the solution to the inequality. Inequality Graph Table Solution a. 5 2x 9 b. 3x 6 > 8 c. 2x + 1 x 2
13 Topic 15: Solving linear inequalities 77 Inequality Graph Table Solution d. 5x + 6 < 8x In question 1, you used the graphing capability of the graphing calculator and the table feature of the graphing calculator to solve several inequalities. What are the advantages and disadvantages of each method? 3. Did one method seem easier for a particular inequality than the other method? Explain.
14 78 Unit 5 Linear equations and inequalities HOMEWORK 15.3 Notes or additional instructions based on whole class discussion of homework assignment: 1. Use tables and a graph to find the x values that make the inequality 2x + 3 > x 1 true. a. Tables: x y = 2x + 3 x y = x Solution: b. Graph: Solution: c. Which method, using a table or a graph, did you find more helpful in solving this inequality? Explain. 2. Nikki and Amber were solving the inequality x + 5 <  3x 1. They created the tables shown. Nikki said the solution was x  1. Amber said the solution was x <  2. Is either of them correct? Explain. x y = x x y =  3x
15 Topic 15: Solving linear inequalities 79 STAYING SHARP 15.3 Practicing algebra skills & concepts 1. Consider this inequality: 2x > 5x a. List three values you can substitute for x to make the inequality statement true. b. List three values you can substitute for x to make the inequality statement false. 2. List the lines according to the value of their slopes. List them in order from the smallest slope value to the largest slope value. Consider the function rules y = 3x + 1 and y = 6x Graph both functions on the coordinate plane. Label each line with its algebraic rule. Answer: Preparing for upcoming lessons 4. Substitute the x and y values of the intersection point into both function rules to verify that the coordinates make both rules true. Focus skill: Slope and geometric connections A lattice point has x and y coordinates that are both integers. 5. Mark two lattice points that are on the line. 6. Draw a slope triangle between the points you marked, and use the slope triangle to calculate the slope of the line. Slope of line:
16 80 Unit 5 Linear equations and inequalities
17 Topic 15: Solving linear inequalities 81 Lesson 15.4 Solving with algebraic operations 15.4 OPENER 1. Complete each inequality statement with the correct symbol, either < or >. 2 < < < < < < < < < What do you notice about the relationship between the answers you get when you add the same number to 2 and to 8? 3. What do you notice about the relationship between the answers you get when you subtract the same number from 2 and from 8? 15.4 CORE ACTIVITY 1. Complete each inequality statement with the correct symbol, either < or > Study the pattern in question 1. When do you need to reverse the inequality sign? 3. Solve the equation 2x + 5 = 11 using algebraic operations. 4. Using the balance scale as a model and the fact that 2x + 5 weighs less than 11, explain why each of the following statements is true. a. 2x will weigh less than 6. b. x will weigh less than 3.
18 82 Unit 5 Linear equations and inequalities 5. Solve 8 2x 14 by first subtracting 8 from both sides. Then complete solving the inequality. 6. This time, solve the inequality 8 2x 14 by first adding 2x to both sides. 7. What do you notice about the processes you used to answer questions 5 and 6? 8. Use inverse operations and algebraic properties to solve the following inequalities. Use substitution to check your solutions. a. 8a 5 1 b. 6b 1 > 3b + 8 c. 0.25(16 12c) 31 d. 1 e e e. 3 < 3( 5d + 16) f. 5f + 4(f 1) 2 + 5(2 + f) 2
19 Topic 15: Solving linear inequalities CONSOLIDATION ACTIVITY 1. Jacob solved four different inequalities, but he is not sure whether he solved them correctly. In fact, sometimes he makes more than one mistake when solving! Jacob s work is shown below. Decide whether Jacob solved each inequality correctly. If not, find the mistake(s) and explain what Jacob did wrong. Then, solve the inequality correctly. Jacob s solution: a. 3x + 6 > 8 3x ( 6) > 8 + ( 6) 3x < 2 3x 3 < 2 3 x < 2/3 Did Jacob solve correctly? If not, describe his mistake(s): Show the correct solution (if needed): b. 2x + 1 x 2 2x x + 1 x x 2 1x x x 3 c. 4(x + 2) > 5x + 1 4x + 2 > 5x + 1 4x > 5x 1 x > 1! d. 5x + 5 > 10x x > 10x x + 5 > 2x + 30 x ( 5) > 2x ( 5) x > 2x + 25 x x < 2x x < x < x < x 2. On your whiteboard, create your own inequality. Exchange your whiteboard with your partner and solve the problem your partner created. When both you and your partner are finished, discuss your solutions.
20 84 Unit 5 Linear equations and inequalities HOMEWORK 15.4 Notes or additional instructions based on whole class discussion of homework assignment: 1. Solve each of the following inequalities. Use substitution to check your solutions. a. 4 2x 5 x + 1 b. 4 3 x + 7 > 3 c. 2x 3(x + 3) < 14 d. 9x 24x + 45 > 0 e. 3.1x x f. 3x + 2(4x + 2) 2(6x + 1) 2. Suppose your friend is having trouble solving the inequality 2(3x 8) < 5(4 x). Show each step you would take to solve the inequality, and write an explanation of why you are taking that step. 3. Jessica was solving the inequality 4x She used inverse operations. To check her work, she chose a number greater than 1 and substituted it into the original inequality to see if it made a true inequality. The number she chose for x was 2. When she substituted it into the inequality, however, she ended up with an untrue inequality. Explain where Jessica made a mistake. Then solve the problem correctly and check your work. Incorrect solution: 4x x x 4 4x x 1 Check: 4(2) Description of mistake: Corrected solution (with check step):
21 Topic 15: Solving linear inequalities 85 STAYING SHARP On the coordinate plane, sketch a line that has a slope of zero and that passes through the point ( 3,5). Then, write an equation for the line. 2. On the coordinate plane, sketch a line that passes through the points (3, 5) and (3,3). Then write an equation for the line. Practicing algebra skills & concepts Equation of line: Equation of line: Preparing for upcoming lessons Complete these tables to answer questions 3 and 4. Table A Table B y = 2 + 3x y = 4 + 3x a. As x increases by 1, by how much does y increase in Table A? b. As x increases by 1, by how much does y increase in Table B? 4. Will there be a common (x,y) pair in the two tables if the tables are extended? Explain. Use this graph to help you answer questions 5 and Write an equation of the line in slope intercept form. Focus skill: Slope and geometric connections 6. On the line, there is a point with an x coordinate of 7. Find that point s y coordinate. Explain how you found the answer.
22 86 Unit 5 Linear equations and inequalities
23 Topic 15: Solving linear inequalities 87 Lesson 15.5 Inequalities in the plane 15.5 OPENER Match each point with a description of its coordinate. 1. Point A 2. Point B 3. Point C 4. Point D 15.5 CORE ACTIVITY Suppose you and some friends go to the movies and buy some snacks. The snack bar charges $2 for a box of candy and $6 for the combo. The combo is a medium drink and popcorn. 1. If x = the number of boxes of candy purchased and y = the number of combos purchased, write an expression that represents the total amount you could spend at the snack bar on candy and combos. 2. After buying the movie tickets, you have $12 left to spend for snacks. Use your cost expression from question 1 to write an inequality that indicates that you would get change from your snack bar purchase. 3. a. Use substitution to determine whether (5,1) is a solution to the inequality you wrote in question 2. b. What does the coordinate pair (5,1) mean in the context of the problem? 4. Is (2,1) a solution to the inequality 2x + 6y < 12? What does the ordered pair (2,1) mean in the context of the problem?
24 88 Unit 5 Linear equations and inequalities 5. a. Which of the given ordered pairs are solutions to the inequality you wrote in question 2? Explain how you know. (3,2) (0,1) (9, 1) (6, 2) ( 4,2) (5,0) b. What do the solutions mean in the context of the problem? 6. Graph the line 2x + 6y = 12 and plot all of the points listed in question 5. Label points that are solutions to the inequality 2x + 6y < 12 with the letter T and the non solutions with the letter F. Where do all the solutions lie? 7. How would you shade your graph to show ALL the ordered pairs that make the inequality true?
25 Topic 15: Solving linear inequalities Match each of the inequalities with its corresponding graph. Write the inequality in the blank space beneath the graph it represents. y >  5 5x 4y > 20 x < y x <  5 5x 4y 20 5x 4y < 20 Inequality: Inequality: Inequality: Inequality: Inequality: Inequality: 15.5 ONLINE ASSESSMENT Today you will take an online assessment.
26 90 Unit 5 Linear equations and inequalities HOMEWORK 15.5 Notes or additional instructions based on whole class discussion of homework assignment: A snack bar charges $3 for a box of candy and $5 for the combo. The combo is a medium drink and popcorn. 1. Write an expression that represents the total amount you could spend at the snack bar on candy and combos. 2. Suppose you can spend at most $12. Find at least three ordered pair solutions representing the number of boxes of candy and combos you can buy. 3. Suppose you want to spend at least $12. Find at least three ordered pair solutions representing the number of boxes of candy and combos you can buy. 4. Suppose you want to spend exactly $12. Find an ordered pair solution representing the number of boxes of candy and combos you can buy. 5. Using the expression you wrote in question 1, write an equation to represent the situation in question 4, in which you spend exactly $12. Graph the equation. Then plot all seven ordered pair solutions to questions 24 on the graph. a. Describe the region of the graph where you find the solutions to question 2. b. Describe the region of the graph where you find the solutions to question 3. c. Describe the region of the graph where you find the solution to question 4.
27 Topic 15: Solving linear inequalities Tanya s mother will pay for Tanya s entire cell phone bill as long as the usage charge is less than $35 for the month. On Tanya s cell phone plan, the usage charge is $0.15 per text message and $0.10 per minute for calls. a. Write an inequality that expresses the number of text messages Tanya may send, t, and the number of minutes Tanya may talk, m, so that her mother will pay the entire cell phone bill for the month. b. Create a graph showing all of the possible combinations of texts and minutes so that Tanya s mother will pay the entire bill. m t c. Use the graph you constructed to find five possible combinations of texts and minutes that would keep Tanya s usage charge under $35.
28 92 Unit 5 Linear equations and inequalities 7. For each inequality, create a graph showing all of the coordinate pairs that make the inequality true. a. y 1 2 x 3 b. 5x 6y < 30 c. x >  3
29 Topic 15: Solving linear inequalities 93 STAYING SHARP 15.5 Practicing algebra skills & concepts 1. Solve the following inequality for x: 8x Answer with supporting work: 2. Write an equation for a line that has a slope of 4 and passes through the point (1,6). Then, name the coordinates of one other point that the line passes through. Answer with supporting work: Preparing for upcoming lessons 3. Report the point of intersection for the graph. Include the context of the situation represented in the graph. Intersection point: 4. The functions y = 2x + 4 and y = 2x + 1 are graphed here. How can you tell from their equations that the two lines will never intersect each other? Answer: Focus skill: Slope and geometric connections 5. Graph the line with a y intercept of (0, 2) and a slope of 4 on the coordinate plane. (Consider using slope 3 triangles to graph efficiently.) 6. Write an equation of the line you graphed in question 5.
30 94 Unit 5 Linear equations and inequalities
31 Topic 15: Solving linear inequalities 95 Lesson 15.6 Compound inequalities in the plane 15.6 OPENER 1. Graph the following compound inequality on a number line: x <  1 or x > 4 2. Graph the following inequalities on the plane: a. x <  1 b. x > 4 3. Using the graphs you constructed in questions 1 and 2, predict what the graph of x <  1 or x > 4 would look like in the plane. Sketch your prediction. Explain why you think your graph is correct.
32 96 Unit 5 Linear equations and inequalities 15.6 CORE ACTIVITY 1. How close was your prediction of the graph of x <  1 or x > 4 in the plane to the correct graph? Explain. 2. Graph the inequality x >  2 and x < 7 on the number line. 3. Graph the inequality x >  2 and x < 7 on the plane. How is the graph related to the graph you constructed in question 2? 4. For each inequality, create a graph showing all of the coordinate pairs that make the inequality true. a. y  4 b. x Graph the following compound inequalities in the plane: a. y  4 or x  2 b. y  4 and x REVIEW ONLINE ASSESSMENT
33 Topic 15: Solving linear inequalities 97 You will work with your class to review the online assessment questions. Problems we did well on: Skills and/or concepts that are addressed in these problems: Problems we did not do well on: Skills and/or concepts that are addressed in these problems: Addressing areas of incomplete understanding Use this page and notebook paper to take notes and re work particular online assessment problems that your class identifies. Problem # Work for problem: Problem # Work for problem: Problem # Work for problem:
34 98 Unit 5 Linear equations and inequalities HOMEWORK 15.6 Notes or additional instructions based on whole class discussion of homework assignment: Next class period, you will take an end of unit assessment. One good study skill to prepare for tests is to review the important skills and ideas you have learned. Use this list to help you review these skills and concepts, especially by reviewing related course materials. Important skills and ideas you have learned in the unit Linear equations and inequalities: Analyze situations involving linear functions and formulate linear equations and inequalities to solve problems Use various methods to solve linear equations and inequalities: inspection, tables, graphs, and use of algebraic operations in connection with the properties of equality Interpret and determine the reasonableness of solutions to linear equations for given contexts Apply techniques for solving equations in one variable to solve literal equations Graph solutions to linear inequalities in one variable on a number line Graph solutions to linear inequalities in two variables on a coordinate plane Graph solutions of compound linear inequalities in two variables on a coordinate plane Homework Assignment Part I: Study for the end of unit assessment by reviewing the key ideas listed above. Part II: Complete the online More practice in the topic Solving linear inequalities. Note the skills and ideas for which you need more review, and refer back to related activities and animations from this topic to help you study. Part III: Complete Staying Sharp 15.6
35 Topic 15: Solving linear inequalities 99 STAYING SHARP a. Find a number that satisfies the inequality x < Write an equation for a line that passes through the points (3,5) and (6,3). Practicing algebra skills & concepts b. Check if the number you found in part a also satisfies the inequality 3x < 9. c. Will any number that satisfies x < 3 also satisfy 3x < 9? Explain. Answer with supporting work: Preparing for upcoming lessons 3. Complete this input output table for both function rules. x y = 4x + 18 y = 2x A classmate has been away and missed several lessons. Explain to that classmate how to use the table you created in question 3 to find the intersection point of the two function rules, and how to check that the coordinates of that intersection point are correct. Focus skill: Slope and geometric connections 5. A line passes through the point (2,3) and has a slope of 2. Graph the line on the coordinate grid. (Consider using slope triangles to graph efficiently.) 6. Write an equation of the line you graphed in question 5.
36 100 Unit 5 Linear equations and inequalities
37 Topic 15: Solving linear inequalities 101 Lesson 15.7 Checking for understanding 15.7 OPENER Bianca and Joe are starting their own pet grooming business called House of Groom. They figure that they can spend no more than $50 a month on pet shampoo. A local dealer of pet shampoo, The Pet Pantry, sells quart bottles of shampoo for $4.00 a bottle plus a $5.00 handling fee per order. 1. Write an expression that represents the amount of money charged by The Pet Pantry for an order of shampoo. 2. Write an inequality that represents the amount House of Groom is willing to pay per month for The Pet Pantry's shampoo. 3. Solve the inequality you wrote in question 2 using any method ENDOFUNIT ASSESSMENT Today you will take the end of unit assessment.
38 102 Unit 5 Linear equations and inequalities 15.7 CONSOLIDATION ACTIVITY 1. For each numbered card, find a match using the lettered cards. Record the matches here. 2. Answer the following questions to reflect on your performance and effort this unit. a. Summarize your thoughts on your performance and effort in math class over the course of this unit of study. Which areas were strong? Which areas need improvement? What are the reasons that you did well or did not do as well as you would have liked? b. Set a new goal for the next unit of instruction. Make your goal SMART. Description of goal: Description of enabling goals that will help you achieve your goal:
39 Topic 15: Solving linear inequalities 103 HOMEWORK 15.7 Notes or additional instructions based on whole class discussion of homework assignment: 1. Explain the phrase compound inequality in the plane in your own words. 2. Graph each compound inequality on the coordinate plane provided. a. x < 5 and x >  3 b. y < 4 and y 0 c. x  2 and y < 3 d. y <  5 or y > 5 e. x 7 or x >2 f. y  3 or x  1
40 104 Unit 5 Linear equations and inequalities STAYING SHARP 15.7 Practicing algebra skills & concepts 1. A line with a slope of 1 passes through the point 3 (3,6). Write an equation for this line. Answer with supporting work: 2. Which of the following points are on the line with equation y = 1 2 x + 7? (4,5) ( 4,3) (4,3) ( 4,5) Preparing for upcoming lessons 3. Graph the function rules y = 4x 3 and y = 2x + 9 on the coordinate plane. Then write the coordinates of their point of intersection. 4. Complete this input output table for the function rules. x y = 4x 3 y = 2x a. For what x value are the y values of the two functions equal? b. How does your answer to question 4a relate to your answer to question 3? Focus skill: Slope and geometric connections Intersection point: 5. Use slope triangles to graph each function rule on the coordinate grid. a. y = 1 2 x + 2 b. y = 2 3 x In which quadrant do the two lines intersect?
Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles
Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and
More informationGeorgia Common Core GPS Coordinate Algebra Supplement: Unit 2 by David Rennie. Adapted from the Georgia Department of Education Frameworks
Georgia Common Core GPS Coordinate Algebra Supplement: Unit 2 by David Rennie Adapted from the Georgia Department of Education Frameworks Georgia Common Core GPS Coordinate Algebra Supplement: Unit 2 by
More informationUNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES. Solving Equations and Inequalities in One Variable
UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES This unit investigates linear equations and inequalities. Students create linear equations and inequalities and use them to solve problems. They
More informationStudy Guide For use with pages 63 68
2.1 For use with pages 63 68 GOAL Use properties of addition and multiplication. VOCABULARY Lesson 2.1 Commutative Property of Addition: In a sum, you can add the numbers in any order. Associative Property
More informationAlgebra 1 Fall Semester Final Review Name
It is very important that you review for the Algebra Final. Here are a few pieces of information you want to know. Your Final is worth 20% of your overall grade The final covers concepts from the entire
More informationWriting and Solving Equations
Writing and Solving Equations Melody s Music Solution Lesson 61 Modeling and Writing TwoStep Equations ACTIVITY 6 Learning Targets: Use variables to represent quantities in realworld problems. Model
More informationInequalities Chapter Test
Inequalities Chapter Test Part 1: For questions 19, circle the answer that best answers the question. 1. Which graph best represents the solution of 8 4x < 4 A. B. C. D. 2. Which of the following inequalities
More informationEvaluate and Simplify Algebraic Expressions
TEKS 1.2 a.1, a.2, 2A.2.A, A.4.B Evaluate and Simplify Algebraic Expressions Before You studied properties of real numbers. Now You will evaluate and simplify expressions involving real numbers. Why? So
More informationMath 3 Variable Manipulation Part 7 Absolute Value & Inequalities
Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,
More informationChapter 4: Systems of Equations and Inequalities
Chapter 4: Systems of Equations and Inequalities 4.1 Systems of Equations A system of two linear equations in two variables x and y consist of two equations of the following form: Equation 1: ax + by =
More informationLesson 1: Writing Equations Using Symbols
COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8 4 Lesson 1: Writing Equations Using Symbols Classwork Exercises Write each of the following statements using symbolic language. 1. The sum of four consecutive
More informationChapter Two B: Linear Expressions, Equations, and Inequalities
Chapter Two B: Linear Expressions, Equations, and Inequalities Index: A: Intro to Inequalities (U2L8) Page 1 B: Solving Linear Inequalities (U2L9) Page 7 C: Compound Inequalities (And) (U2L10/11) Page
More informationAlgebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations. Unit Calendar
Algebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations Unit Calendar Date Topic Homework Nov 5 (A ) 6.1 Solving Linear Inequalities +/ 6.2 Solving Linear Inequalities x/ 6.3 Solving
More informationUnit 4: Inequalities. Inequality Symbols. Algebraic Inequality. Compound Inequality. Interval Notation
Section 4.1: Linear Inequalities Section 4.2: Solving Linear Inequalities Section 4.3: Solving Inequalities Applications Section 4.4: Compound Inequalities Section 4.5: Absolute Value Equations and Inequalities
More informationChapter Four: Linear Expressions, Equations, and Inequalities
Chapter Four: Linear Expressions, Equations, and Inequalities Index: A: Intro to Inequalities (U2L8) B: Solving Linear Inequalities (U2L9) C: Compound Inequalities (And) (U2L10/11) D: Compound Inequalities
More informationLesson 7: Literal Equations, Inequalities, and Absolute Value
, and Absolute Value In this lesson, we first look at literal equations, which are equations that have more than one variable. Many of the formulas we use in everyday life are literal equations. We then
More informationGrade 8 + DIGITAL. EL Strategies. DOK 14 RTI Tiers 13. Flexible Supplemental K8 ELA & Math Online & Print
Standards PLUS Flexible Supplemental K8 ELA & Math Online & Print Grade 8 SAMPLER Mathematics EL Strategies DOK 14 RTI Tiers 13 1520 Minute Lessons Assessments Consistent with CA Testing Technology
More informationEssential Question How can you solve an absolute value inequality? Work with a partner. Consider the absolute value inequality x
Learning Standards HSACED.A.1 HSAREI.B.3.6 Essential Question How can you solve an absolute value inequality? COMMON CORE Solving an Absolute Value Inequality Algebraically MAKING SENSE OF PROBLEMS To
More informationUnit 1: Introduction to Variables
Section 1.1: Writing Algebraic Expressions Section 1.2: The Story of x Section 1.3: Evaluating Algebraic Expressions Section 1.4: Applications Section 1.5: Geometric Formulas KEY TERMS AND CONCEPTS Look
More informationThis is a review packet for the entire fall semester of Algebra I at Harrison.
HARRISON HIGH SCHOOL ALGEBRA I Fall Semester Review Packet This is a review packet for the entire fall semester of Algebra I at Harrison. You are receiving it now so that: you will have plenty of time
More informationDefine the word inequality
Warm Up: Define the word inequality Agenda: Objective Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two
More information4. The table shows the number of toll booths driven through compared to the cost of using a Toll Tag.
ALGEBRA 1 Fall 2016 Semester Exam Review Name 1. According to the data shown below, which would be the best prediction of the average cost of a bedroom house in Georgetown in the year 2018? Year Average
More information7 = 8 (Type a simplified fraction.)
Student: Date: Assignment: Exponential and Radical Equations 1. Perform the indicated computation. Write the answer in scientific notation. 3. 10 6 10. 3. 4. 3. 10 6 10 = (Use the multiplication symbol
More informationWhen a graph on a coordinate plane is a straight line that goes through the origin it is called a direct
DIRECT VARIATION TABLES AND SLOPE LESSON 3B When a graph on a coordinate plane is a straight line that goes through the origin it is called a direct variation graph. In this lesson you will investigate
More informationSerena: I don t think that works because if n is 20 and you do 6 less than that you get 20 6 = 14. I think we should write! 6 > 4
24 4.6 Taking Sides A Practice Understanding Task Joaquin and Serena work together productively in their math class. They both contribute their thinking and when they disagree, they both give their reasons
More informationLesson 22 ~ Parallel, Intersecting or the Same Line
Lesson ~ Parallel, Intersecting or the Same Line Graph the two linear equations in each system on a single coordinate plane and state whether the lines are intersecting, parallel or the same line.. x 5
More informationLinear Functions, Equations, and Inequalities
CHAPTER Linear Functions, Equations, and Inequalities Inventory is the list of items that businesses stock in stores and warehouses to supply customers. Businesses in the United States keep about.5 trillion
More informationManipulating Radicals
Lesson 40 Mathematics Assessment Project Formative Assessment Lesson Materials Manipulating Radicals MARS Shell Center University of Nottingham & UC Berkeley Alpha Version Please Note: These materials
More informationWriting and Graphing Inequalities
.1 Writing and Graphing Inequalities solutions of an inequality? How can you use a number line to represent 1 ACTIVITY: Understanding Inequality Statements Work with a partner. Read the statement. Circle
More informationName Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the xintercept.
61 Reteaching Graphing is useful for solving a system of equations. Graph both equations and look for a point of intersection, which is the solution of that system. If there is no point of intersection,
More information11. Variables and Expressions. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
 Variables and Expressions Vocabulary Review What mathematical operation is shown in each equation? Write addition, subtraction, multiplication, or division.. 6? 2 5 2 2. 4 2 4 5 0. 27 4 5 9 4. 7 5 20
More informationALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Algebra 1 S1 (#2201) and Foundations in Algebra 1 S1 (#7769)
Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Ramal goes to the grocery store and buys pounds of apples and pounds of bananas. Apples cost dollars per
More informationPattern & Algebra Practice Problems
Pattern & Algebra Practice Problems Solve Linear Inequalities 1. Solve for x. A. x > 3 B. x > 0 C. x < 0 D. x < 3 4x < 6 + 2x Symbolize Problem Situations 2. Scott is draining his swimming pool. The
More informationAlgebra 1 Practice Test. Algebra 1. Practice Test. Copyright Karin Hutchinson, All rights reserved.
Algebra 1 Practice Test Copyright Karin Hutchinson, 2011. All rights reserved. Please respect the time, effort, and careful planning spent to prepare these materials. The distribution of this ebook via
More informationCRS SKILL LEVEL DESCRIPTION
GRE 501 LESSON/NOTES Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must GRE 301 Locate points on the number line attain mastery at this level R XEI 506 Solve first degree inequalities that
More informationMore with Systems of Equations
More with Systems of Equations In 2008, 4.7 million Americans went on a rafting expedition. In Georgia, outfitters run whitewater expeditions for ages 8 and up on the Chattooga River. 12.1 Systems of Equations
More informationAlgebra 1 PAP Fall Exam Review
Name: Pd: 20162017 Algebra 1 PAP Fall Exam Review 1. A collection of nickels and quarters has a value of $7.30. The value of the quarters is $0.80 less than triple the value of the nickels. Which system
More informationCOMPOUND INEQUALITIES
13 (3 1) Chapter 3 Inequalities in One Variable 95. Designer jeans. A pair of ordinary jeans at AMart costs $50 less than a pair of designer jeans at Enrico s. In fact, you can buy four pairs of AMart
More informationName ALGEBRA 1 MODULE When factored completely, which is a factor of 12a 2 3a?
Name ALGEBRA MODULE. When factored completely, which is a factor of 2a 2 3a? a. 2a b. (4x 2 + ) c. 3a d. (4x ) 2. Simplify: a. 4 b. 2 ( x 7) xx ( 4) 2 7x 7 2x 3 c. x 3 d. x 7 x 3 3. A person s hair is
More informationACTIVITY: Simplifying Algebraic Expressions
. Algebraic Expressions How can you simplify an algebraic expression? ACTIVITY: Simplifying Algebraic Expressions Work with a partner. a. Evaluate each algebraic expression when x = 0 and when x =. Use
More informationGRADE 7 MATH LEARNING GUIDE. Lesson 26: Solving Linear Equations and Inequalities in One Variable Using
GRADE 7 MATH LEARNING GUIDE Lesson 26: Solving Linear Equations and Inequalities in One Variable Using Guess and Check Time: 1 hour Prerequisite Concepts: Evaluation of algebraic expressions given values
More informationBuilding Concepts: Solving Systems of Equations Algebraically
Lesson Overview In this TINspire lesson, students will investigate pathways for solving systems of linear equations algebraically. There are many effective solution pathways for a system of two linear
More information(2 x 23x + 5) + ( x 2 + 6x  4) = 3 x 2 + 3x + 1 (continued on the next page)
Algebra Lab Adding and Subtracting Polynomials Monomials such as 3x and x are called like terms because they have the same variable to the same power. When you use algebra tiles, you can recognize like
More informationAlgebra I Notes Linear Inequalities in One Variable and Unit 3 Absolute Value Equations and Inequalities
PREREQUISITE SKILLS: students must have a clear understanding of signed numbers and their operations students must understand meaning of operations and how they relate to one another students must be able
More informationThe Benchmarks MA.912.A.3.14 and MA.912.A.3.15 are limited to a maximum of two variables in Algebra I, Algebra IH, Algebra Ib,
Algebra I Florida EOC Study Guide You are allowed to use the Algebra I EOC FCAT reference sheet (Attached) on the exam. This exam is computerbased. View the epat Algebra I Practice Test for more information.
More informationSolving Equations by Adding and Subtracting
SECTION 2.1 Solving Equations by Adding and Subtracting 2.1 OBJECTIVES 1. Determine whether a given number is a solution for an equation 2. Use the addition property to solve equations 3. Determine whether
More informationChapter Systems of Equations
SM1 Name: 011314 Date: Hour: Chapter 6.16.4 Systems of Equations 6.1 Solving Systems by Graphing CCS A.REI.6: Solve systems of equations exactly and approximately (e.g. with graphs), focusing on pairs
More informationInstructional Materials for WCSD Math Common Finals
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: High School Algebra 1 S1
More informationy in both equations.
Syllabus Objective: 3.1 The student will solve systems of linear equations in two or three variables using graphing, substitution, and linear combinations. System of Two Linear Equations: a set of two
More informationName: Period: Date: Algebra 1 1st Semester Review Which best describes the solution(s) for this equation? 3 ( 8x 12) = 33 2x
Name: Period: ate: lgebra 1 1st Semester Review 2011 1 Which algebraic expression could NOT match the pictorial representation below? 5 Which best describes the solution(s) for this equation? 3 ( 8x 12)
More informationSilver Spring International Middle School Algebra Summer Packet
Name: Silver Spring International Middle School Algebra Summer Packet It is NOT mandatory to complete but, STRONGLY encouraged. MONTGOMERY COUNTY PUBLIC SCHOOLS SILVER SPRING INTERNATIONAL MIDDLE SCHOOL
More informationAlgebra I Summer Review Packet
Algebra I Summer Review Packet DUE THE FIRST DAY OF CLASS Name: Dear Algebra I Students and Parents, The problems in this packet are designed to help you review topics that are important to your success
More informationAlgebra 1 S1 (#2201) Foundations in Algebra 1 S1 (#7769)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: Algebra 1 S1 (#2201) Foundations
More informationName: Class: Date: ID: A. c. the quotient of z and 28 z divided by 28 b. z subtracted from 28 z less than 28
Name: Class: Date: ID: A Review for Final Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Give two ways to write the algebraic expression z 28 in words.
More informationName: Period: Unit 3 Modeling with Radical and Rational Functions
Name: Period: Unit Modeling with Radical and Rational Functions 1 Equivalent Forms of Exponential Expressions Before we begin today s lesson, how much do you remember about exponents? Use expanded form
More informationLesson 14: Solving Inequalities
Student Outcomes Students learn ifthen moves using the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line. Classwork Exercise 1 (5
More informationSection 4 Topic 1 Arithmetic Sequences
Section 4 Topic 1 Arithmetic Sequences Let s look at the following sequence of numbers: 3, 8, 13, 18, 23,.... Ø Ø Ø The at the end means that this sequence goes on forever. 3, 8, 13, 18, and 23 are the
More informationMoving Straight Ahead  Unit Test Review Sheet
Name: Class: Date: ID: A Moving Straight Ahead  Unit Test Review Sheet Short Answer 1. Use the graph at the right. a. Find the slope of the line. b. Find the equation of the line. 2. Does the table below
More information1Factor binomials that. 2Use the difference. Then. Why? Now. New Vocabulary dif ference of two squares
Then You factored trinomials into two binomials. (Lesson 83, 8) New Vocabulary dif ference of two squares Now Quadratic Equations: Differences of Squares 1Factor binomials that are the difference of
More informationSolving MultiStep Inequalities
 What You ll Learn To solve multistep inequalities with variables on one side To solve multistep inequalities with variables on both sides... And Why To find the measurements of a banner, as in Eample
More informationEquations and Inequalities in One Variable
Name Date lass Equations and Inequalities in One Variable. Which of the following is ( r ) 5 + + s evaluated for r = 8 and s =? A 3 B 50 58. Solve 3x 9= for x. A B 7 3. What is the best first step for
More informationWriting and Graphing Inequalities
4.1 Writing and Graphing Inequalities solutions of an inequality? How can you use a number line to represent 1 ACTIVITY: Understanding Inequality Statements Work with a partner. Read the statement. Circle
More informationEgyptian Fractions: Part I
Egyptian Fractions: Part I Prepared by: Eli Jaffe October 8, 2017 1 Cutting Cakes 1. Imagine you are a teacher. Your class of 10 students is on a field trip to the bakery. At the end of the tour, the baker
More informationSystems of Linear Equations: Solving by Adding
8.2 Systems of Linear Equations: Solving by Adding 8.2 OBJECTIVES 1. Solve systems using the addition method 2. Solve applications of systems of equations The graphical method of solving equations, shown
More informationEE616 Equivalent Expressions Pages
EE66 Equivalent Expressions Pages 0 STANDARDS 6.EE.A.2, 6.EE.A.3, 6.EE.A. Goals Students will use the area of rectangles and the properties of operations to show that two expressions are equivalent. Vocabulary
More informationEquations and Inequalities
Equations and Inequalities Figure 1 CHAPTER OUTLINE 1 The Rectangular Coordinate Systems and Graphs Linear Equations in One Variable Models and Applications Comple Numbers Quadratic Equations 6 Other Types
More informationWhy? Step 3 Substitute the value from Step 2 into either equation, and solve for the other variable. Write the solution as an ordered pair.
Substitution Then You solved systems of equations by graphing. (Lesson 61) Now 1Solve systems of equations by using substitution. 2Solve realworld problems involving systems of equations by using substitution.
More informationHow can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality
. Solving Inequalities Using Multiplication or Division How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Copy and
More informationCHAPTER 4: SIMULTANEOUS LINEAR EQUATIONS (3 WEEKS)...
Table of Contents CHAPTER 4: SIMULTANEOUS LINEAR EQUATIONS (3 WEEKS)... 2 4.0 ANCHOR PROBLEM: CHICKENS AND PIGS... 6 SECTION 4.1: UNDERSTAND SOLUTIONS OF SIMULTANEOUS LINEAR EQUATIONS... 8 4.1a Class Activity:
More informationLESSON 2 PRACTICE PROBLEMS KEY
LESSON PRACTICE PROBLEMS KEY 1)If x 11= 1, then x = 4 d) 16 x 11 1 4 x 1 4 4 4 x 1 4 x 16 ) If 7x + 6y = 15 and 4x 6y = 18, what is the value of x? a) Line the equations up vertically: 7x 6y 15 4x 6y
More informationName Date Class. Fishing Hook G Kite A is at a height of 21 feet. It ascends 15 feet. At what height is it now?
Name Date Class 1 The Number System Of Kites and Fishing Hooks The heights of kites and the depths of fishing hooks can be recorded using positive and negative integers and rational numbers. Use the table
More informationAlgebra 1 ECA Remediation Diagnostic Homework Review #2
Lesson 1 1. Simplify the expression. (r 6) +10r A1.1.3.1 Algebra 1 ECA Remediation Diagnostic Homework Review # Lesson. Solve the equation. 5x + 4x = 10 +6x + x A1..1 Lesson 3. Solve the equation. 1 +
More informationAlgebra 1 Enriched Midterm Review
Algebra 1 Enriched Midterm Review Know all vocabulary, pay attention to the highlighted words in the text, and understand the various types of directions in each of the sections of the textbook. Practice
More informationN5 R1.1 Linear Algebra  Revision
N5 R Linear Algebra  Revision This revision pack covers the core linear algebra skills and provides opportunities to apply these skills to standard and challenging exam level questions. This pack is not
More informationDraw a horizontal line. Place a point on the line and label it 0.
Lesson 1 Materials: Paper, Ruler, Compass Activity: Constructing the Number Line: Draw a horizontal line. Place a point on the line and label it 0. Use a compass to locate and label the next point 1, thus
More informationUnit 3 Linear Algebra & Unit 4 Systems of Linear Equations REVIEW. + is equal to 2.
Unit 3 Linear Algebra & Unit 4 Systems of Linear Equations REVIEW 1. The expression 3x + 5y 7x+ 4y is equivalent to which of the following? 1. (1) 4x 9y () 9y 4 x (3) 4x y (4) 10x + 9y. Written without
More informationand Transitional Comprehensive Curriculum. Algebra II Unit 4: Radicals and the Complex Number System
011 and 0114 Transitional Comprehensive Curriculum Algebra II Unit 4: Radicals and the Complex Number System Time Frame: Approximately three weeks Unit Description This unit expands student understanding
More informationMath 1 Variable Manipulation Part 5 Absolute Value & Inequalities
Math 1 Variable Manipulation Part 5 Absolute Value & Inequalities 1 ABSOLUTE VALUE REVIEW Absolute value is a measure of distance; how far a number is from zero: 6 is 6 away from zero, and " 6" is also
More informationInequalities. and Graphing Inequalities 4.3 Solving Inequalities Using. What would you have?
Inequalities.1 Writing ii in and Graphing Inequalities. Solving Inequalities Using Addition or Subtraction. Solving Inequalities Using Multiplication or Division. Solving TwoStep Inequalities If you reached
More informationSolving Equations with Variables on Both Sides
1. Solving Equations with Variables on Both Sides Essential Question How can you solve an equation that has variables on both sides? Perimeter Work with a partner. The two polygons have the same perimeter.
More informationHonors Algebra 2 Summer Practice Problems 2017
Honors Algebra II Summer Assignment 017 These are the directions for your summer assignment for next year s course. This is an opportunity for you to review selected topics from Algebra One to make sure
More informationAlgebra II A Guided Notes
Algebra II A Guided Notes Name Chapter 1 Period Notes 15 Learning Matrix Goal #9: I can solve inequalities. Learning Matrix Goal #10: I can solve realworld problems involving inequalities. Learning Matrix
More informationCLASS NOTES: BUSINESS CALCULUS
CLASS NOTES: BUSINESS CALCULUS These notes can be thought of as the logical skeleton of my lectures, although they will generally contain a fuller exposition of concepts but fewer examples than my lectures.
More informationYou discovered in Lesson 4.1 that when two powers with the same base are multiplied, the base remains the
Division Properties of Exponents Lesson 4.2 You discovered in Lesson 4.1 that when two powers with the same base are multiplied, the base remains the same and the exponents are added together. Examine
More informationUnit 5: Moving Straight Ahead
Unit 5: Moving Straight Ahead Investigation 3 Solving Equations I can recognize problem situations in which two variables have a linear relationship and solve rate of change problems. In the last Investigation,
More informationSection 2 Topic 1 Equations: True or False?
Section 2: Equations and Inequalities Section 2 Topic 1 Equations: True or False? Consider the statement 4 + 5 = 2 + 7. This is a mathematically correct sentence. Is the sentence true or false? True Consider
More informationBeginning Algebra. v. 1.0
Beginning Algebra v. 1.0 Table of Contents About the Author... 1 Acknowledgments... 2 Preface... 3 Chapter 1: Real Numbers and Their Operations... 5 Real Numbers and the Number Line... 6 Adding and Subtracting
More informationVariables and Patterns: Homework Examples from ACE
Variables and Patterns: Homework Examples from ACE Investigation 1: Variables, Tables, and Graphs ACE #7 Investigation 2: Analyzing Relationships among Variables, ACE #17 Investigation 3: Relating Variables
More informationAlgebra 1 STAAR Review Name: Date:
Algebra 1 STAAR Review Name: Date: 1. Which graph does not represent y as a function of x? I. II. III. A) I only B) II only C) III only D) I and III E) I and II 2. Which expression is equivalent to? 3.
More informationWhy? Speed Skating Tracks offi cial track short track
Applying Systems of Linear Equations Then You solved systems of equations by using substitution and elimination. (Lessons 62, 63, and 64) Now 1Determine the best method for solving systems of 2Apply
More informationGearing Up for Geometry!
Gearing Up for Geometry! Geometry is right around the corner and you need to make sure you are ready! Many of the concepts you learned in Algebra I will be used in Geometry and you will be epected to remember
More informationSections 8.1 & 8.2 Systems of Linear Equations in Two Variables
Sections 8.1 & 8.2 Systems of Linear Equations in Two Variables Department of Mathematics Porterville College September 7, 2014 Systems of Linear Equations in Two Variables Learning Objectives: Solve Systems
More informationAlgebra I H Semester 1 Practice Exam
4. Find the product: 8 0 5 7 5 4 0 40 5 48 48 40 4 0 40 5 5 4 0 5 7 5 4 4 0 5 7 48 5. Find the difference of the matrices:. Which boxandwhisker plot below represents the following set of data: {0, 4,,
More informationLesson 22: Solving Equations Using Algebra
Student Outcomes Students use algebra to solve equations (of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers); using techniques of making zero (adding the additive
More informationIntroductory Algebra Final Exam Review
Note: This review represents the topics covered by the final exam. It is in no way intended to represent the quantity of any particular type of problem on the final exam. The answers and graph paper are
More informationChapter 4  Writing Linear Functions
Chapter 4  Writing Linear Functions Write an equation of the line with the given slope and yintercept. 1. slope: 3 yintercept: 6 a. y = 6x + 3 c. y = 6x 3 b. y = 3m + 6 d. y = 3x 6 2. D REF: Algebra
More information8th Grade Thanksgiving Packet Student Name: Teacher Name: Jalethea Howard Date: Score: 1 )) Solve for z. A) z = 4 B) z = 6 C) z = 8 D) z = 4.8 5 z 8 = 3 2 2 )) Find the measure of G. A) 50 B) 54 C) 60
More informationCCGPS UNIT 1 Semester 1 COORDINATE ALGEBRA Page 1 of 33. Relationships Between Quantities Name:
CCGPS UNIT 1 Semester 1 COORDINATE ALGEBRA Page 1 of 33 Relationships Between Quantities Name: Date: Reason quantitatively and use units to solve problems. MCC912.N.Q.1 Use units as a way to understand
More informationLESSON #11  FORMS OF A LINE COMMON CORE ALGEBRA II
LESSON #  FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS
More informationPreAlgebra Semester 1 Practice Exam A
. Evaluate xy when x 0 and y 6. 6 80. Which expression is equivalent to x x x xxx x x xxx x x?. In math class, we follow the order of operations when evaluating expressions. Which is the second operation
More information