New Vocabulary equivalent inequalities. x 1 4, 7 and x, 3 are equivalent inequalities.
|
|
- Randall Walters
- 6 years ago
- Views:
Transcription
1 -. Plan - Solving Inequalities Using Addition and Subtraction Objectives To use addition to solve To use subtraction to solve Eamples Using the Addition Property of Inequality Solving and Checking Solutions Using the Subtraction Property of Inequality Real-World Problem Solving Math Background What You ll Learn To use addition to solve To use subtraction to solve... And Why To solve a problem involving safe loads, as in Eample Check Skills You ll Need GO for Help Lesson - and Review page 8 Complete each statement with R,, or S. S R S Solve each equation.. 9. n 6. t 9 7. k 6 6 New Vocabulary equivalent Part Using Addition to Solve Inequalities Equivalent are with the same solutions. For eample,, 7 and, are equivalent. Students may have used a balance scale to model equations. Here it may help them to solve if they refer to an unbalanced scale. More Math Background: p. 98C Lesson Planning and Resources See p. 98E for a list of the resources that support this lesson. PowerPoint Bell Ringer Practice Check Skills You ll Need For intervention, direct students to: Adding Rational Numbers Lesson -: Eample Etra Skills and Word Problems Practice, Ch. Solving One-Step Equations Review p. 8: Eample You can add the same value to each side of an inequality, just as you did with equations. Using the Addition Property of Inequality Solve,. Graph the solution., Add to each side., 8 + < 7 < Key Concepts Property Addition Property of Inequality For every real number a, b, and c, if a. b, then a c. b c; if a, b, then a c, b c. Eamples., so..,, so,. This property is also true for $ and #. Simplify Solve m 6.. Graph your solution. m S ; 0 06 Chapter Solving Inequalities 06 Special Needs L To help students understand infinity, use the number line in Eample. Ask: What number is to the right of 0? of? Then ask: Will there ever be a number that does not have yet another number to its right? No learning style: visual Below Level L Present students with several pairs of and their solutions. Have students take turns eplaining what was done to each inequality to produce its solution. learning style: verbal
2 Vocabulary Tip The word infinite indicates that the number of solutions is unlimited. The solutions cannot be listed. An inequality has an infinite number of solutions, so it is not possible to check all the solutions. You can check your computations and the direction of the inequality symbol. The steps below show how to check that < 8 describes the solutions to Eample. Step Check the computation. See if 8 is the solution to the equation. 8 0 Substitute 8 for. Step Check the inequality symbol. Choose any number less than 8 and substitute it into,. In this case, use 7. < 7 < Substitute 7 for. < Since the computation and the direction of the inequality symbol are correct,, and, 8 are equivalent. So the solution of, is, 8. Solving and Checking Solutions Solve #. Graph and check your solution. # Add to each side. 7 # Simplify.. Teach Guided Instruction Tactile Learners Let students use tiles to model the inequality. Have students write the inequality sign on an inde card. Instruct them to place the card between the two sets of tiles. Then have them solve the inequality. When the solution is complete, students can check by substituting tiles for a value of in the original model. Special Needs L Remind students that the dot and arrow in Eample means that 7 and all numbers to the right of 7 on the number line are solutions to the inequality For: Linear Inequalities Activity Use: Interactive Tetbook, - Check Check the computation. 0 7 Substitute 7 for. # Check the direction of the inequality. # 8 Substitute 8 for. # Solve n 7 #. Graph and check your solution. n K ; Part Using Subtraction to Solve Inequalities You can subtract the same number from each side of an inequality to create an equivalent inequality. Key Concepts Property Subtraction Property of Inequality For every real number a, b, and c, if a. b, then a c. b c; if a, b, then a c, b c. Eamples., so.,, so, This property is also true for $ and #. Lesson - Solving Inequalities Using Addition and Subtraction 07 Advanced Learners L Have students discuss whether is equivalent to - - and eplain each step of their reasoning. learning style: verbal English Language Learners ELL Be sure students understand how the solution of an equation differs from the solution of an addition or subtraction inequality. Ask them to compare and to give a real-world eample of each. learning style: verbal 07
3 PowerPoint Additional Eamples Solve p -. Graph the solution. p R 0 6 Using the Subtraction Property of Inequality Solve y,7. Graph the solution. y,7 Subtract from each side. y, Simplify. Solve 8 $ d -. Graph and check your solution. 0 L d, or d K Solve t $ 8. Graph and check your solution. t L ; You can use to model real-world situations. 0 6 Guided Instruction Real-World Problem Solving Diversity Some students may have lived in a shelter or may live in one now. Be sure other students are sensitive when discussing the question. PowerPoint Additional Eamples Solve c + 7. Graph the solution. c S 0 In order to receive a B in your literature class, you must earn more than 0 points of reading credits. Last week you earned 0 points. This week you earned 90 points. How many more points must you earn to receive a B? points Resources Daily Notetaking Guide - L Daily Notetaking Guide - Adapted Instruction L Closure Ask students to compare solving using addition and subtraction with solving equations using addition and subtraction. In both cases, you must add or subtract the same amount to or from both sides. A B C D E A B C D E A B C D E A B C D E A B C D E B C D E Test-Taking Tip You can test inequality choices by substituting a reasonable value for the variable. If the value is NOT a solution of the inequality you can eliminate that choice as the correct answer. EXERCISES Eamples, (pages 06, 07) 08 Chapter Solving Inequalities Multiple Choice The maimum safe load of a chairlift is 680 lb. In the spring, a cyclist and bicycle go to the top of the slope using the chairlift. The weight of the person is lb, and the weight of the bicycle is lb. Which inequality best describes how much additional weight w the chairlift could safely carry? Relate Define Let Practice and Problem Solving A GO Practice by Eample for Help w # 680 w $ 680 weight of a person and a bicycle w plus Write additional weight the amount of weight that can be added to the chairlift. The inequality w # 680 models the situation. So B is the correct answer. Your baseball team has a goal to collect at least 60 blankets for a shelter. Team members brought blankets on Monday and 6 blankets on Wednesday. Write an inequality to describe how many blankets the team must donate on Friday to make or eceed their goal. ± 6 ± b 60, or b State what number you would add to each side of the inequality to solve the inequality.. d $. 0, c 8 8. z. $.6. w w # 680 w $ 680 is at most Solve each inequality. Graph and check your solution. 6. See margin t, 6.. b 7. 7 # d 8. s $6 9. r 9 # , n. $ w., d. y #.. q. $ r 7... m.8 8. b, 9. n See back of book. # safe load 680 For more eercises, see Etra Skill and Word Problem Practice. 08 pages 08 Eercises. S 9 0. t R 0 6. b R d L s L 9. r K 9 0. n S
4 B Eample (page 08) Eample (page 08) Apply Your Skills 6c. Answers may vary. Sample: The sign means the sides are equal, so the two sides may be interchanged. The R sign does not indicate equality. One side cannot be both greater than and less than the other side. Real-World Connection More than 7,000 athletes compete in gymnastic programs in the United States.. w K. d S State what number you would subtract from each side of the inequality to solve the inequality. 0. w.. 8, r..7 $ k.. Solve each inequality. Graph and check your solution. 8. See back of book.. w # 9. m.., 8 b 6. $ a 7. r $ 8. k # , p. z $. 7. y,., m..7 $ a..9,. p 6. $ h 7.. d t, Vacation Budget Your brother has $000 saved for a vacation. His airplane ticket is $67. Write and solve an inequality to find how much he can spend for everything else. s ± 67 K 000, $6 0. Weekly Budget You have an allowance of $.00 per week. You are in a bowling league that costs $6.0 each week, and you save at least $.00 each week. Write and solve an inequality to show how much you have left to spend each week. s ± 6.0 ± K, $.0. Fund-Raising A school club is selling reflectors for Bicycle Safety Day. Each member is encouraged to sell at least 0 reflectors. You sell 7 on Monday and on Tuesday. How many reflectors do you need to sell on Wednesday to meet your goal? r ± 7 ± L 0, reflectors State what you must do to the first inequality in order to get the second.. 6 # y; 0# y. 9 b. ; b.. m, ; m, Add to each side. Subtract 9 from each side. Add to each side. Solve each inequality.. w $ 9 w L 6. c # c K 7. y 0.,.8 y R n n R 9. z., y 0.9 z R 9.7. t y R t S 6. # v 7 v L 6..6 k $. k L b 7, b R 6. m. #. 6. $ k k K m K. 7. h $ h L $ K w w R 60. Banking Your local bank offers free checking for accounts with a balance of at least $00. Suppose you have a balance of $6.6 and you write a check for $.96. How much must you deposit to avoid being charged a service fee? at least $.0 6. a. If 7 t, does t 7? yes b. If 7, r, is r, 7? no c. Discuss the differences between these two eamples. See above left. 6. Gymnastics Suppose your sister wants to qualify for a regional gymnastics GPS competition. At today s competition she must score at least.0 points. She scored 8.8 on the vault, 7.9 on the balance beam, and 8. on the uneven parallel bars. The event that remains is the floor eercise. a b. See back of book. a. Write and solve an inequality that models the information. b. Eplain what the solution means in terms of the original situation. c. Open-Ended Write three scores your sister could make that would allow her to qualify for the regional gymnastics competition. Answers may vary. Sample: 9., 9., 9. lesson quiz, PHSchool.com, Web Code: ata-00 Lesson - Solving Inequalities Using Addition and Subtraction y K. q R L. 6. r R Practice Assignment Guide A B -9, -, 67-7 A B 0-, -66, 7 C Challenge 7-78 Test Prep 79-8 Mied Review 8-97 Homework To check students understanding of key skills and concepts, go over Eercises 8, 9, 6, 6, 7. Error Prevention! Eercises 9 Some students may have difficulty deciding in which direction to draw the graph of a solution. Point out that when the solution has the variable on the left, the graph points in the same direction as the inequality symbol. When the solution has the variable on the right, the graph points in the opposite direction of the inequality symbol. Eercises 8 Suggest to students that they eliminate the fractions or decimals before solving. GPS Enrichment Guided Problem Solving Reteaching Adapted Practice Practice Pearson Education, Inc. All rights reserved. Name Class Date Practice - Each pair of figures is similar. Find the length of Use a proportion to solve nabc is similar to nxyz. The length AB is 0. The length BC is 7. Find the length XY if the length YZ is. 0. Marty has a scale model of a car. The scale is in. : in. If the model is 6.7 in. long, how long is the actual car?. A blueprint scale is in. : ft. The width of a building is 8 ft. What is the width of the building on the blueprint?. Angie is using similar triangles to find the height of a tree. A stick that is ft tall casts a shadow that is ft long. The tree casts a shadow that is ft long. How tall is the tree?. nabc is similar to nxyz. The length AC is 0. The length BC is 6. What is the length XZ if the length YZ is?. A map has a scale of in. : mi. Two cities are 7 mi apart. How far apart are they on the map? Proportions and Similar Figures 7 6. L L L L L 09
5 . Assess & Reteach PowerPoint Lesson Quiz Solve each inequality. Graph the solutions.. p - 7 $ - p L 0. w - -9 w R S 0. $ 9 + h L h, or h K 0 Alternative Assessment Group students in pairs. Instruct each student to model an inequality using tiles and an inde card with the inequality sign written on it. Have students echange with their partners and find the solutions. Encourage students to check their solutions. 66b. Answers may vary. Sample: Substituting values does not work because there is always the possibility that the solution lies between values that make the inequality true and a value that does not. Real-World C Connection In 97, a computer chip could hold 00 transistors. In 00, a chip could hold 0,000,000 transistors. 7. not true; sample countereample: for a and b 6, ( 6) ±( 6) GO nline Homework Help Visit: PHSchool.com Web Code: ate not true; sample countereample: for a 0, b, and c, 0 R and 0 ± ( ) Challenge 7d. The length of the third side must be greater than the difference of the lengths of the other two sides. 6. Computers Suppose your computer has nearly 6 megabytes (MB) of memory. Its basic systems require.8 MB. How much memory is available for other programs and functions? nearly. MB 6. To earn an A in Ms. Orlando s math class, students must score a total of at least points on the three tests. On the first two tests, Amy s scores were 7 and 8. What is the minimum score she must get on the third test to earn an A? 0 points 6. a. Open-Ended Use each of the inequality symbols,, #,., and $ to write four addition or subtraction. a b. Check students work. b. Solve each of the in part (a) and graph your solution. 66. a. Sam says that he can solve z 8.6 $. by replacing z with,, and. When z, the inequality is false. When z and z, the inequality is true. So Sam says that the solution is z $. Is his reasoning correct? Justify your answer. No; the solution is z L.8, so z L is not correct. b. Critical Thinking Eplain why substituting values into the inequality does not guarantee that your solution is correct. See margin. Solve each inequality. 67. $ L 68. n 6n, n R 69. 7t (6t ) # t K 70. k (k ). 8 k S (a ) 7a # a K 7. (a ) (a ), a R 8 7. Geometry The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Following are for sides of the triangle shown. a b. c b c. a a c. b a. Write an inequality using c b and a. a S c b b. Write an inequality using a c and b. b S a c c. Write an inequality using b a and c. c S b a d. Writing Write a generalization about the length of the third side and the difference of the lengths of the other two sides. See left. Reasoning Decide if each inequality is true for all real numbers. If the inequality is not true, give a countereample. 7. a b, a b See above left. 7. If a $ b, then a c $ b c. true 76. If c. d, then a c, a d. true 77. If a, b, then a, b c. See above left. 78. Reasoning Find real numbers, y, z, and w for which it is true that. y and z. w, but it is not true that z. y w. Answers may vary. Sample: For, y, z, and w, S and S, but. a c b Test Prep Multiple Choice 79. Solve,. B A.. 8 B., 8 C.. 8 D., Solve - n. 0. G F. n, G. n. H. n, 8 J. n. 8 0 Chapter Solving Inequalities 0
6 8. [] at least points; (9.) ± S (0) 68 ± S 00 S (OR equivalent eplanation) [] incorrect answer OR no work or eplanation Short Response 8. Which graph represents all real number solutions of $ 8? A A. B. 0 0 C. D Which of the following is a solution for, n 0.? J F..99 G..0 H..0 J.. 8. Hector is flying his plane. To avoid a storm, he climbs 00 ft without going above his plane s maimum safe altitude of,000 ft. The inequality a 00 #,000 represents his original altitude a in feet. Which of the following could have been the original altitude? D A. 0,00 ft B. 0,000 ft C. 9,70 ft D. 7,70 ft 8. The leading scorer in your high school s basketball division finished the season with a game average of 0 points for games. As the division s second leading scorer, you have a 9. point per game average for games. You have your last game yet to play. How many points must you score in the final game of the season to overtake the division s leading scorer? Show your work. See above left. Test Prep Resources For additional practice with a variety of test item formats: Standardized Test Prep, p. 7 Test-Taking Strategies, p. Test-Taking Strategies with Transparencies Eercise 8 Point out to students that they can quickly eliminate answer choices B and D, since these have open dots. Mied Review GO for Help Lesson - Lesson - Define a variable and write an inequality to model each situation. 8. An octopus can be up to 0 ft long. Let c length of octopus in feet. c K A hummingbird migrates more than 80 mi. Let h distance in miles a hummingbird migrates. h S Your average in algebra class must be 90 or greater for you to receive an A for the term. Let a average. a L You must read at least pages this weekend. Let p number of pages to read. p L Simplify ( ) (..) ? ( ) (6 ) Algebra at Work Marketing Director Marketing directors rely on equations and to predict the actions their companies must take to stay competitive. For eample, the marketing director of a manufacturing company determines how much the cost of raw materials can increase before the company must raise the price of its finished goods or services. The director also predicts the effect of price changes on the quantity of goods and services sold by his company. PHSchool.com For: Information about a career in marketing Web Code: atb-0 Lesson - Solving Inequalities Using Addition and Subtraction
Patterns and Functions. Write an algebraic expression for each phrase more than twice a number 2. a number divided by 4
- Patterns and Functions -. Plan What You ll Learn To write a function rule To understand relationships of quantities in a function... And Why To find reasonable domain and range for real-world situations,
More informationWhat You ll Learn. or irrational. New Vocabulary perfect square, square root, irrational numbers, real numbers. Why Learn This?
-. Plan - Exploring Square Roots and Irrational Numbers Objective To find and estimate square roots and to classify numbers as rational or irrational Examples Finding Square Roots of Perfect Squares Estimating
More informationWrite in simplest form. New Vocabulary rate of change
-. Plan bjectives To find rates of change from tables and graphs To find slope Eamples Finding Rate of Change Using a Table Finding Rate of Change Using a Graph Finding Slope Using a Graph Finding Slope
More informationSolving Multi-Step Inequalities
- What You ll Learn To solve multi-step inequalities with variables on one side To solve multi-step inequalities with variables on both sides... And Why To find the measurements of a banner, as in Eample
More informationNew Vocabulary inductive reasoning conjecture counterexample. Using Inductive Reasoning
-. Plan - Patterns and Inductive Reasoning Objectives To use inductive reasoning to make conjectures Examples Finding and Using a Patternn Using Inductive Reasoning 3 Finding a Counterexample Real-World
More informationCircles in the Coordinate Plane. Find the length of each segment to the nearest tenth y. Distance Formula Square both sides.
-5 ircles in the oordinate Plane -5. Plan What You ll Learn To write an equation of a circle To find the center and radius of a circle... nd Wh To describe the position and range of three cellular telephone
More informationEXAMPLE EXAMPLE. Simplify. Simplify each expression. See left. EXAMPLE Real-World Problem Solving EXAMPLE. Write = xa1 1!5 B = 162 Cross multiply.
-. Plan Lesson Preview Check Skills You ll Need Operations With Radical Epressions Lesson -: Eamples,, 7 Eercises, Etra Practice, p. 7 Lesson Preview What You ll Learn - To simplify sums and differences
More informationUNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:
UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities
More informationUnderstanding and Using Variables
Algebra is a powerful tool for understanding the world. You can represent ideas and relationships using symbols, tables and graphs. In this section you will learn about Understanding and Using Variables
More informationName Class Date. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Practice - Solving Two-Step Equations Solve each equation. Check your answer.. a +. +. b +. 9 + t. a +. -t + Write an equation to model each situation. Then solve.. You want to buy a bouquet of yellow
More informationSimplifying a Rational Expression. Factor the numerator and the denominator. = 1(x 2 6)(x 2 1) Divide out the common factor x 6. Simplify.
- Plan Lesson Preview Check Skills You ll Need Factoring ± ± c Lesson -5: Eamples Eercises Etra Practice, p 70 Lesson Preview What You ll Learn BJECTIVE - To simplify rational epressions And Why To find
More informationChapter 9: Equations and Inequalities
Chapter 9: Equations and Inequalities Lesson Objectives Class Periods Tetbook & Workbook Teacher's Guide Page Additional Materials Needed Determine whether a given number makes an equation true. TB: 28
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 informationSolutions of Linear Equations
Lesson 14 Part 1: Introduction Solutions of Linear Equations Develop Skills and Strategies CCSS 8.EE.C.7a You ve learned how to solve linear equations and how to check your solution. In this lesson, you
More informationLooking Ahead to Chapter 4
Looking Ahead to Chapter Focus In Chapter, you will learn about functions and function notation, and you will find the domain and range of a function. You will also learn about real numbers and their properties,
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 informationMathematics. Standards Plus. Grade COMMON CORE INTERVENTION SAMPLER
Mathematics Standards Plus COMMON CORE INTERVENTION Grade 7 SAMPLER Standards Plus COMMON CORE INTERVENTION Available for Grades 1-8 Language Arts and Math Standards Plus COMMON CORE INTERVENTION Mathematics
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 informationSection 2.2 Objectives
Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational
More informationEssential Question: How can you solve equations involving variable exponents? Explore 1 Solving Exponential Equations Graphically
6 7 6 y 7 8 0 y 7 8 0 Locker LESSON 1 1 Using Graphs and Properties to Solve Equations with Eponents Common Core Math Standards The student is epected to: A-CED1 Create equations and inequalities in one
More informationPre-Algebra Semester 1 Practice Exam B DRAFT
. Evaluate x y 5 6 80 when x = 0 and y =.. Which expression is equivalent to? + + + +. In Pre-Algebra class, we follow the order of operations in evaluating expressions. Which operation should a student
More information7.2 Multiplying Polynomials
Locker LESSON 7. Multiplying Polynomials Teas Math Standards The student is epected to: A.7.B Add, subtract, and multiply polynomials. Mathematical Processes A.1.E Create and use representations to organize,
More informationFinding Complex Solutions of Quadratic Equations
COMMON CORE y - 0 y - - 0 - Locker LESSON 3.3 Finding Comple Solutions of Quadratic Equations Name Class Date 3.3 Finding Comple Solutions of Quadratic Equations Essential Question: How can you find the
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 informationAdding and Subtracting Rational Expressions
COMMON CORE Locker LESSON 9.1 Adding and Subtracting Rational Epressions Name Class Date 9.1 Adding and Subtracting Rational Epressions Essential Question: How can you add and subtract rational epressions?
More informationEquations Quadratic in Form NOT AVAILABLE FOR ELECTRONIC VIEWING. B x = 0 u = x 1 3
SECTION.4 Equations Quadratic in Form 785 In Eercises, without solving the equation, determine the number and type of solutions... In Eercises 3 4, write a quadratic equation in standard form with the
More informationWrite an inequality for the graph. Then, in words, describe all the values of x that make the inequality true
Name Date. Practice A Write an inequality for the graph. Then, in words, describe all the values of that make the inequality true... 6 8 0 6 Write the word sentence as an inequality.. A number is at most..
More informationAnalyze Scatter Plots. How can you analyze data displayed on a scatter plot?
? Name 1. Essential Question nalyze Scatter Plots How can you analyze data displayed on a scatter plot? ata nalysis 5.9. MTHEMTIL PROESSES 5.1., 5.1., 5.1.F Unlock the Problem You can use a scatter plot
More informationHow can you use multiplication or division to solve an equation? ACTIVITY: Finding Missing Dimensions
7.3 Solving Equations Using Multiplication or Division How can you use multiplication or division to solve an equation? 1 ACTIVITY: Finding Missing Dimensions Work with a partner. Describe how you would
More informationSOLVING LINEAR INEQUALITIES
Topic 15: Solving linear inequalities 65 SOLVING LINEAR INEQUALITIES Lesson 15.1 Inequalities on the number line 15.1 OPENER Consider the inequality x > 7. 1. List five numbers that make the inequality
More informationMath 7 Homework # 46 M3 L1
Name Date Math 7 Homework # 46 M3 L1 Lesson Summary Terms that contain exactly the same variable symbol can be combined by addition or subtraction because the variable represents the same number. Any order,
More information6.2 Multiplying Polynomials
Locker LESSON 6. Multiplying Polynomials PAGE 7 BEGINS HERE Name Class Date 6. Multiplying Polynomials Essential Question: How do you multiply polynomials, and what type of epression is the result? Common
More informationUsing a Graphing Calculator
Using a Graphing Calculator Unit 1 Assignments Bridge to Geometry Name Date Period Warm Ups Name Period Date Friday Directions: Today s Date Tuesday Directions: Today s Date Wednesday Directions: Today
More informationReteaching Using Deductive and Inductive Reasoning
Name Date Class Reteaching Using Deductive and Inductive Reasoning INV There are two types of basic reasoning in mathematics: deductive reasoning and inductive reasoning. Deductive reasoning bases a conclusion
More informationUnit 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 informationSection 2.3 Objectives
Section 2.3 Objectives Use the inequality symbols to compare two numbers. Determine if a given value is a solution of an inequality. Solve simple inequalities. Graph the solutions to inequalities on the
More informationSolving Inequalities
Solving Inequalities Inequalities and Their Graphs Objective: To write, graph, and identify solutions of inequalities. Objectives I can write an inequality. I can identify solutions by evaluating inequalities.
More informationA function is a rule that establishes a relationship between two quantities, called
1.7 An Introduction to Functions What you should learn GOAL 1 Identify a function and make an input-output table for a function. GOAL 2 Write an equation for a real-life function, such as the relationship
More informationAlgebra I Solving & Graphing Inequalities
Slide 1 / 182 Slide 2 / 182 Algebra I Solving & Graphing Inequalities 2016-01-11 www.njctl.org Slide 3 / 182 Table of Contents Simple Inequalities Addition/Subtraction click on the topic to go to that
More informationDomain, Range, and End Behavior
Locker LESSON 1.1 Domain, Range, and End Behavior Common Core Math Standards The student is epected to: F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship
More informationCommon Core State Standards for Activity 14. Lesson Postal Service Lesson 14-1 Polynomials PLAN TEACH
Postal Service Lesson 1-1 Polynomials Learning Targets: Write a third-degree equation that represents a real-world situation. Graph a portion of this equation and evaluate the meaning of a relative maimum.
More informationEXAMPLE EXAMPLE. Quick Check
- Biconditionals and Definitions -. Plan What You ll Learn To write biconditionals To recognize good definitions... And Why To evaluate definitions of letters used in the American Manual Alphabet, as in
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 informationExpressions and. equation. Algebra Expressions 3.2 Adding and Subtracting Linear Expressions. Descartes, if you solve for. in the equation, what do
Expressions and Equations.... Algebra Algebraic Algebra Expressions. Adding and Subtracting Linear Expressions. Solving Equations Using Addition or Subtraction. Solving Equations Using Multiplication or
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 informationName Class Date. You can use the properties of equality to solve equations. Subtraction is the inverse of addition.
2-1 Reteaching Solving One-Step Equations You can use the properties of equality to solve equations. Subtraction is the inverse of addition. What is the solution of + 5 =? In the equation, + 5 =, 5 is
More informationUnit 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 informationReview: Expressions and Equations
Review: Expressions and Equations Expressions Order of Operations Combine Like Terms Distributive Property Equations & Inequalities Graphs and Tables Independent/Dependent Variables Constant: a number
More informationSimple Inequalities Involving Addition and Subtraction. Unit 3 Inequalities.notebook. November 18, Table of Contents
Table of Contents Simple Inequalities Addition/Subtraction Simple Inequalities Multiplication/Division Two-Step and Multiple-Step Inequalities Solving Compound Inequalities Special Cases of Compound Inequalities
More informationWriting and Solving Equations
Writing and Solving Equations Melody s Music Solution Lesson 6-1 Modeling and Writing Two-Step Equations ACTIVITY 6 Learning Targets: Use variables to represent quantities in real-world problems. Model
More information1 st : Read carefully and underline key words 2 nd : Write a let statement 3 rd : Determine whether to use,,, or 4 th : Write and solve the inequality
Name Period: Represent each of the following as an algebraic inequality. 1) x is at most 30 2) the sum of 5x and 2x is at least 14 3) the product of x and y is less than or equal to 4 4) 5 less than a
More information8 th Grade Algebra 5 Day Lesson Plan. *Computer* *Pan Scale* *Algebra Tiles* *Equation Mat* *TI-83 Plus/ TI-73* Karen Kmiotek
8 th Grade Algebra 5 Day Lesson Plan *Computer* *Pan Scale* *Algebra Tiles* *Equation Mat* *TI-83 Plus/ TI-73* Karen Kmiotek Objectives Students will be able to solve equations by using algebra and the
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 informationSolving Linear Systems
1.4 Solving Linear Sstems Essential Question How can ou determine the number of solutions of a linear sstem? A linear sstem is consistent when it has at least one solution. A linear sstem is inconsistent
More informationPre-Algebra Semester 1 Practice Exam A
. Evaluate y when = 0 and y = 6. 5 6 80. Which epression is equivalent to 5 5 + + + + + 5?. In math class, we follow the order of operations when evaluating epressions. Which is the second operation a
More informationReady To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities
A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear
More informationUnit 5: Proportions and Lines. Activities: Resources:
Timeline: 2 nd nine weeks Vocabulary: Slope Formula, Rate of Change, Y Intercept, Slope intercept form, Vertical, Horizontal Linear Function Slope Slope of a Line Unit 5: Proportions and Lines New State
More informationMATH 110: FINAL EXAM REVIEW
MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set
More informationSchool District of Palm Beach County. Summer Packet Algebra EOC Review
School District of Palm Beach County Summer Packet Algebra EOC Review Summer 2014 Students and Parents, This Summer Packet for Algebra 1 EOC Review is designed to provide an opportunity to review and remediate
More informationLINEAR EQUATIONS Modeling Linear Equations Common Core Standards
E Linear Equations, Lesson 1, Modeling Linear Functions (r. 2018) LINEAR EQUATIONS Modeling Linear Equations Common Core Standards F-BF.A.1 Write a function that describes a relationship between two quantities.
More informationTEACHER GUIDE VOLUME 1. Larry Bradsby. Chapter 3, Objective 2
TEACHER GUIDE VOLUME Larry Bradsby Chapter 3, Objective 2 Solving Linear Equations In this chapter, students begin to solve basic linear equations using addition, subtraction, multiplication, division,
More information8.2 Graphing More Complicated Rational Functions
1 Locker LESSON 8. Graphing More Complicated Rational Functions PAGE 33 Name Class Date 8. Graphing More Complicated Rational Functions Essential Question: What features of the graph of a rational function
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 informationinequalities Solutions Key _ 6x 41 Holt McDougal Algebra 1 think and discuss 2-1 Check it out! b w 4-4 w
CHAPTER Inequalities Solutions Key Are You Ready?. B. E. F. D. C 6. b - a = 6 - = 7. ab = ()(6) = 9. a + b = + 6 = 8 8. b a = 6 =. .. % =..
More informationWords to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression
1 Words to Review Give an example of the vocabulary word. Numerical expression 5 1 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression
More informationFocusing on Linear Functions and Linear Equations
Focusing on Linear Functions and Linear Equations In grade, students learn how to analyze and represent linear functions and solve linear equations and systems of linear equations. They learn how to represent
More informationMATH 021 UNIT 1 HOMEWORK ASSIGNMENTS
MATH 01 UNIT 1 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usuall, the part (A) questions ask for eplanations,
More informationName Algebra 1 Midterm Review Period. = 10 4x e) x ) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16
Name Algebra 1 Date Midterm Review Period 1) Solve each equation: a) x 2x + 2 = 3 b) 5 5 + 9 = 13 c) 64 = 9x +1 d) x 7 2 = 10 4x e) x + 2 3 = 3x 2) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16 3) Solve and
More informationSolving and Graphing Linear Inequalities Chapter Questions. 2. Explain the steps to graphing an inequality on a number line.
Solving and Graphing Linear Inequalities Chapter Questions 1. How do we translate a statement into an inequality? 2. Explain the steps to graphing an inequality on a number line. 3. How is solving an inequality
More informationName Period Date DRAFT
Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,
More informationFoundations for Algebra. Introduction to Algebra I
Foundations for Algebra Introduction to Algebra I Variables and Expressions Objective: To write algebraic expressions. Objectives 1. I can write an algebraic expression for addition, subtraction, multiplication,
More informationEssential Question How can you determine the number of solutions of a linear system?
.1 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A.3.A A.3.B Solving Linear Sstems Using Substitution Essential Question How can ou determine the number of solutions of a linear sstem? A linear sstem is consistent
More informationWords to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression
1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression
More informationMath 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 3. Functions Worksheet III 15
Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)
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 8-3, 8-) New Vocabulary dif ference of two squares Now Quadratic Equations: Differences of Squares 1Factor binomials that are the difference of
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 informationContents. To the Teacher... v
Katherine & Scott Robillard Contents To the Teacher........................................... v Linear Equations................................................ 1 Linear Inequalities..............................................
More informationTeacher Resource Sampler. Algebra 1. Common Core. MatPri111484CCSSAlg1ResourceSampler.indd 1
Teacher Resource Sampler Algebra 1 Common Core MatPri111484CCSSAlg1ResourceSampler.indd 1 6/3/11 :04 PM Going beyond the textbook with Pearson Algebra 1 Common Core Edition provides the teacher with a
More informationBishop Kelley High School Summer Math Program Course: Algebra 2 A
06 07 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 6 pages of this packet provide eamples as to how to work some of the problems
More information6 th Grade - TNREADY REVIEW Q3 Expressions, Equations, Functions, and Inequalities
6 th Grade - TNREADY REVIEW Q3 Expressions, Equations, Functions, and Inequalities INSTRUCTIONS: Read through the following notes. Fill in shaded areas and highlight important reminders. Then complete
More informationALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6
ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6 FALL 2014 0 1 Algebra 1 Section 6.1 Notes: Graphing Systems of Equations System of Equations: a set of two or more equations with the same variables, graphed in the
More informationEnhanced Instructional Transition Guide
Enhanced Instructional Transition Guide / Unit 05: Suggested Duration: 9 days Unit 05: Algebraic Representations and Applications (13 days) Possible Lesson 01 (4 days) Possible Lesson 02 (9 days) POSSIBLE
More informationALGEBRA 1 SUMMER ASSIGNMENT
Pablo Muñoz Superintendent of Schools Amira Presto Mathematics Instructional Chair Summer Math Assignment: The Passaic High School Mathematics Department requests all students to complete the summer assignment.
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II 1 st Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 1 st Nine Weeks, 2016-2017 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More information1-2 Study Guide and Intervention
1- Study Guide and Intervention Real Numbers All real numbers can be classified as either rational or irrational. The set of rational numbers includes several subsets: natural numbers, whole numbers, and
More informationGrade 8. Functions 8.F.1-3. Student Pages
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 Functions 8.F.1-3 Student Pages 2012 2012 COMMON CORE CORE STATE STATE STANDARDS ALIGNED ALIGNED MODULES Grade 8 - Lesson 1 Introductory Task
More informationCurriculum Scope & Sequence Subject/Grade Level: MATHEMATICS/GRADE 7 Course: MATH 7
BOE APPROVED 3/12/13 Curriculum Scope & Sequence Subject/Grade Level: MATHEMATICS/GRADE 7 Course: MATH 7 Unit Duration NJCCCS / Unit Goals Transfer Goal(s) Enduring Review of 10 Days Unit Goals: There
More informationQuiz For use after Section 4.2
Name Date Quiz For use after Section.2 Write the word sentence as an inequality. 1. A number b subtracted from 9.8 is greater than. 2. The quotient of a number y and 3.6 is less than 6.5. Tell whether
More information2.6 The Distributive Property
Page 1 of 8 2.6 The Distributive Property What you should learn GOAL 1 Use the distributive property. GOAL 2 Simplify epressions by combining like terms. Why you should learn it To solve real-life problems
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabulary Define each term in your own words.. function 2. linear function 3. independent variable 4.
More informationChapter 3 Notes Algebra 1
Chapter 3 Notes Algebra 1 name per (3-1) INEQUALITIES/ : any number that can make an inequality true. GRAPHS x < 4 : x 13 : x -6 : x > -9 : Vocabulary: x is.. 8 less than greater than less than or equal
More informationReady to Go On? Skills Intervention Integers in Real-World Situations
11-1 Ready to Go On? Skills Intervention Integers in Real-World Situations Positive numbers are greater than 0. They can be shown with or without the positive sign. For example: 25 or 25 Negative numbers
More informationHolt Algebra 1. Know-It Notebook TM
Holt Algebra 1 Know-It Notebook TM Copyright by Holt, Rinehart and Winston No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including
More informationProportional and Nonproportional Situations
L E S S N. Florida Standards The student is epected to: Functions.F.1. Compare properties of two functions each represented in a different wa (algebraicall, graphicall, numericall in tables, or b verbal
More informationHonors Math 2 Unit 7: Modeling Advanced Functions
Honors Math Unit 7: Modeling Advanced Functions Name: Model situations using inverse variation (F-BF.1) Explain why a solution is extraneous and give examples of extraneous solutions (A-REI.) Create equations
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 informationLinear Functions. Essential Question How can you determine whether a function is linear or nonlinear?
. Linear Functions Essential Question How can ou determine whether a function is linear or nonlinear? Finding Patterns for Similar Figures Work with a partner. Cop and complete each table for the sequence
More information28 (Late Start) 7.2a Substitution. 7.1b Graphing with technology Feb 2. 4 (Late Start) Applications/ Choosing a method
Unit 7: Systems of Linear Equations NAME: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay attention and
More informationEureka Math Module 4 Topic G Solving Equations
Eureka Math Module 4 Topic G Solving Equations Lessons 23-27 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make
More informationACTIVITY: Using a Table to Plot Points
.5 Graphing Linear Equations in Standard Form equation a + b = c? How can ou describe the graph of the ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $6 worth of tickets
More information