Unit 3. Solving: Literal Equations, Compound Inequalities, & Absolute Value Equations/Inequalities. Algebra I

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1 Algebra I Unit 3 Solving: Literal Equations, Compound Inequalities, & Absolute Value Equations/Inequalities Name: Lesson 3-A Solving Literal Equations Notes Practice 1 Practice 2 Lesson 3-B Solving Compound Inequalities Notes Part 1 Practice 1 Notes Part 2 Practice 2 Practice 3 Lesson 3-C Solving Absolute Value Equations & Inequalities Notes Practice 1 Practice 2 Unit 2 Study Guide

2 Unit 3 Extra Practice Problems If you want more practice on any section, here are some practice problems from your book. The answers to these problems are in the back of your book so you can check your work and track your own understanding Lesson 3-A - Literal Equations (Ch. 2-8): Page Odd, 9 17 Odd, 21, 23, 29, 31 Lesson 3-B - Compound Inequalities (Ch. 5-4): Page Odd Lesson 3-C - Absolute Value Equations (Ch. 2-5): Absolute Value Inequalities (Ch. 5-5): Page Odd Page Odd Check the website (tinyurl.com/tunderwood) for additional videos and resources as we progress through the unit. Don t forget the online book has Personal Tutor Videos for examples at the beginning of each of these chapters Check it out

3 Lesson 3-A Notes (2-8) Algebra 1 Literal Equations TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI. 3 Solve equations and inequalities in one variable. Past Target I solved one-step equations, multistep equations and equations with variables on each side. Present Target I can solve equations or formulas for a specified variable. Future Target I will solve for y to graph linear equations using slope-intercept form. 1. Put a box around the letter you are solving for. 2. Work backwards order of operations as you did before Ex. 1 - Solve each equation. Ex. 2 - Solve each equation or formula for the specified variable. a. a. 5 = 30 a. = ", solvefor b. 7 = b. =, solvefor c. 10 = 14 c. 3 = h, solvefor d. = 4 d. h =, solveforh

4 e. 20 = e. = 2 + 2, solvefor f. 8 = 22 f. =, solvefor g. " = 38 g. = 4, solvefor h = h. 7 + = 5 +, solvefor Ex. 3 - The formula for converting Fahrenheit temperatures to Celsius tempertures is = ( 32), where F is the Fahrenheit temperature and C is the Celsius temperature. a. Solve the formula for F. b. What is the Fahrenheit temperature if the Celsius temperature is 30?

5 Ex. 4 - The formula for volume of a rectangular prism is = ", where is the length, is the width and is the height. a. Solve the formula for. b. Find the length of the rectangular prism that has a volume of 180 cubic feet, a width of 6 and height of 10. Ex. 5 - List the steps to solve the following equation for. NOTE: You may not need all of the lines = Ex. 6 Error Analysis Sandra and Fernando are solving 4 5 = 7 for. Is either of them correct? Explain with words why each person is either correct or incorrect. Sandra 4 5 = = = 7 Fernando 4 5 = = =

6 Lesson 3-A Algebra 1 - Practice 1 Solving Literal Equations Part 1 Solve each equation. Solve each equation or formula for the specified variable. 1a. 2x =13 1b. = ", solvefor Name: Date: 2a. 4 = x 2 2b. t = d, solve for d r 3a. x + 6 = 10 3b. 1 m + p = n, solve for m 2 4a. 3x + 2 = 17 4b. = 2 + 2, solvefor 5a. 5x 6 = 9 5b. 2x 4y = 6, solve for y

7 6a. 9 = 3( 1 + x) 6b. V = x( 1+ p), solve for p Part 2 7. Acceleration is the measure of how fast a velocity is changing. The formula for acceleration is =, where a represents the acceleration rate, is the final velocity, is the initial velocity and represents the time in seconds. a. Solve the formula for. b. What is the final velocity of a runner who is accelerating at 2 feet per second squared for 3 seconds with an initial velocity of 4 feet per second? 8. The formula for calculating the circumference of a circle is = ", where represents the circumference and represents the radius. a. Solve the formula for. b. What is the radius of the circle if the circumference is inches? 9. List the steps to solve the following equation for. NOTE: You may not need all of the lines =

8 Lesson 3-A Practice 2 Algebra 1 Solve each equation or formula for y. SHOW YOUR WORK 1) 2 + = 7 2)8 4 = 4 3) 3 = ) 5 = ) + 5 = 10 6) = 30 7) = 18 8) 5 + = 20 9) 3 21 = 12 10) = 4 11) 2 = 4 12) 2 = 3

Lesson 3-B Notes - Part 1 (5-4) Solving Compound Inequalities TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI. 3 Solve equations and inequalities in one variable.

Future Target I will solve compound inequalities containing the word or, and graph their solution set. *Compound Inequality: 2 or more inequalities that are connected by the words or.

9 Lesson 3-B Notes - Part 1 (5-4) Solving Compound Inequalities TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI. 3 Solve equations and inequalities in one variable. Past Target I solved linear inequalities involving one or more operations. Present Target I can solve compound inequalities containing the words and/or, and graph their solution set. Future Target I will solve compound inequalities containing the word or, and graph their solution set. *Compound Inequality: 2 or more inequalities that are connected by the words or. *Intersection: the graph of a compound inequality containing. *A compound inequality containing AND is true only if inequalities are true. *The intersection can be found by graphing each inequality and determining where the graphs. Ex. 1 - Graph the solution set of each compound inequality and write the solution in set builder notation. a. < 10 and < 5 When we think of an intersection, we normally think of the place where two roads meet. < 10 < 5 If you are standing in the intersection, how many roads are you on?? An intersection makes inequalities true b. 4 < 2 c. < 3" > 1

10 Ex. 2 - Solve each compound inequality. Then graph the solution set. a. 3 < 2 0 Solution Set:. b < 16 2 and 9 < Solution Set:. Ex. 3 - Write a compound inequality for the graph below. Ex. 4 - Write an inequality and solve. A"number"plus"one"is"greater"than"negative"five" and"less"than"three. "

11 Lesson 3-B Practice 1 Algebra 1 Intersection (AND) Compound Inequalities Part 1: Just Graph it Directions: Graph the solution set of each compound inequality. No need to write it in set builder notation 1) > 1" 3 2) 5 2 3) > 3" 4 4) 2 < 4 5) 3 > " < 2 6) 1 3 Part 4: Just Write it Directions: Write a compound inequality in set builder notation for each graph. 7) 8) Part 5: Solve, Graph, and Write it Directions: For each compound inequality, solve, graph, and write the solution in set builder notation 9) 4 < ) 3 5 < 2 11) 4 < ) 1 2" + 2 1

12 13) 2 > 3" + 4 < 6 14) 3 < <

Lesson 3-B Notes - Part 2 (5-4) Solving Compound Inequalities TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI. 3 Solve equations and inequalities in one variable.

13 Lesson 3-B Notes - Part 2 (5-4) Solving Compound Inequalities TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI. 3 Solve equations and inequalities in one variable. Past Target I solved linear inequalities involving one or more operations. I solved compound inequalities containing and, and graphed the solution set. Present Target I can solve compound inequalities containing the word or, and graph their solution set. Future Target I will solve and graph absolute value equations and inequalities. *A compound inequality containing OR is true if at least of the inequalities is true. *Union: the graph of a compound inequality containing. Ex. 1 - Graph the solution set of each compound inequality and write the solution in set builder notation. a. 3" < 2 < 10 A Marriage is often thought of as a UNION, SO MUCH STUFF < 5 In a marriage, everyone brings their stuff with them. Whether it s his, hers, or theirs, it s all included A union solution includes. b. 1" < 5 c. 4" > 0

14 Ex. 2 - Solve each compound inequality. Then graph the solution set. a. 4 < 2 10 or 3 < 12 Solution Set:. b < 16 2 and 9 < Solution Set:. Ex. 3 - Write a compound inequality for the graph below. Ex. 4 - Write an inequality and solve. BIKES The recommended air pressure for the tires of a mountain bike is at least 35 pounds per square inch (psi), but no more than 80 pounds per square inch. If a bike s tires have 24 pounds per square inch, what is the recommended range of air that should be put into the tires?

Part 1: Just Graph it Lesson 3-B Practice 2 Algebra 1 Union (OR) Compound Inequalities Directions: Graph the solution set of each compound inequality.

15 Part 1: Just Graph it Lesson 3-B Practice 2 Algebra 1 Union (OR) Compound Inequalities Directions: Graph the solution set of each compound inequality. No need to write it in set builder notation 1) > 2" 3 4)4 " < 8 2) 5) 3 " 1 3 > " < 2 3) 6) 4" > 0 2 " 3 Part 4: Just Write it Directions: Write a compound inequality in set builder notation for each graph. 7) 8) Part 5: Solve, Graph, and Write it Directions: For each compound inequality, solve, graph, and write the solution in set builder notation 9) 3 < 3"3 9 10) " < 2 11) 12) " < 12" 3 2

16 13) > 2"2 2 < ) "7 + 3 < 2 + 6

17 Lesson 3-C Notes (2.5, 5.5) Absolute Value Equations & Inequalities TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI.3 Solve equations and inequalities in one variable. Past Target I solved multi-step equations and compound inequalities. Present Target I can solve and graph absolute value equations and absolute value inequalities. Future Target I will graph inequalities in two variables. What%is%absolute%value?% Determine%the%absolute%value%of%each%number.%%%%Determine%the%numbers%that%have%the%given%absolute%value.%% a. 45 = b. 24 = c. or =5d. or% =21 A FEW THINGS TO REMEMBER: An absolute value equation or inequality will ALWAYS have problems, since there are directions from zero. Absolute values with a >, are compound inequalities. Think: Great Absolute values with a <, are compound inequalities. Think: Less Th Ex. 1 - Solve each equation / inequality. Then graph the solution set and put it in Set Builder Notation. a. 3 = 12 SolutionGraph: SetBuilderNotation:. c. 3 3 < 9 SolutionGraph: SetBuilderNotation:. b. + 6 > 8 SolutionGraph: SetBuilderNotation:. d SolutionGraph: SetBuilderNotation:.

18 e. + 6 = 10 SolutionGraph: SetBuilderNotation:. f SolutionGraph: SetBuilderNotation:. Ex. 2 - Write an absolute value equation or inequality for each graph. 1. Find the number equidistant from the ends (the middle) The absolute value will be x MINUS this number 2. Find the distance from the middle to the end values this will be your DISTANCE (What it s equal to/less than/greater than) 3. Write your absolute value equation / inequality a. b. c. % Ex. 3 Real World Examples RAINFALL The average annual rainfall in California for the last 100 WEATHER The average January temperature in a northern Canadian years is 23 inches. However, the annual rainfall can differ city is 3 F. The actual temperature for that city may be by 10 inches from the 100-year average. about 6 warmer or colder. a) What is the range of annual rainfall for California? a) What are the maximum and minimum temperatures? b) Graph this range. b) Graph this solution. c) Write the absolute value inequality that describes the situation. c) Write the absolute value inequality that describes the situation.

19 Lesson 3-C Algebra 1 Practice 1 Solving Absolute Value Equations & Inequalities Solve each equation or inequality. Then graph the solution set. 1. " + = " 2. Solution(Graph:((( ( ( ( ( Solution(Graph:((( ( ( ( ( ( ( The(solution(set(is(. The(solution(set(is( > 4. " < Solution(Graph:((( ( ( ( ( Solution(Graph:((( ( ( ( ( ( ( The(solution(set(is(. The(solution(set(is(. 5. " + " 6. + = Solution(Graph:((( ( ( ( ( Solution(Graph:((( ( ( ( ( ( ( The(solution(set(is(. The(solution(set(is(.

20 Lesson 3-C Algebra 1 Practice 2 Solving Absolute Value Equations & Inequalities Solve each equation or inequality. Then graph the solution set. 1. " + = " 2. + " Solution(Graph:((( ( ( ( ( Solution(Graph:((( ( ( ( ( ( ( The(solution(set(is(. The(solution(set(is(. 3. " > 4. + = Solution(Graph:((( ( ( ( ( Solution(Graph:((( ( ( ( ( ( ( The(solution(set(is(. The(solution(set(is( = Solution(Graph:((( ( ( ( ( Solution(Graph:((( ( ( ( ( ( ( The(solution(set(is(. The(solution(set(is(.

21 Name Date Period Unit 3 Test Study Guide Algebra 1 Literal Equations & Compound Equations / Inequalities Lesson 3-A Solve each equation or formula for the variable indicated. SHOW YOUR WORK 1) = ", for 2) h + 7 = 50, "h 3) 5 + = 2, " 4) " =, " 5) = + 32, for 6) = 2 + 2, " 7) 4 + = 8, " 8) = h, for 9) " + " =, for Lesson 3-B Graph the solution set of each compound inequality. 10) > 1" 3 11) 4" > 0 12) 4 1

22 Write a compound inequality in set builder notation for each graph. 13) 14) Write and graph a compound inequality for the following situations. 15) A company is manufacturing an action figure that must be at least 11.2 centimeters and at most 11.4 centimeters tall. Write and graph a compound inequality that describes how tall the action figure can be. 16) A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night, and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort. Solve each compound inequality. Then graph the solution set and write the solution in set builder notation. 17) 9 < < 10 18) 3 8" ) + 8 < 4"3 < 5 20) 10 2 > 12"7 < 4 + 9

21) 3 + 8 < 2" + 12 > 2 22) 2 + 4 6" 2 4 Write an inequality and solve each problem. 23) A number minus one is at most nine, or two times the number is at least twenty-four.

23 21) < 2" + 12 > 2 22) " 2 4 Write an inequality and solve each problem. 23) A number minus one is at most nine, or two times the number is at least twenty-four. 24) Jim is selling gift cards to raise money for a class trip. He can earn prizes depending on how many cards he sells. So far, he has sold 34 cards. How many more does he have to sell to earn a prize in category 4? Lesson 3-C Solve each equation or inequality. Then graph the solution set. 25) ) 5 = 4

27) 3 + 6 = 9 28) + 5 > 7 29) 5ℎ + 2 = 8 30) 8 14 31) 5 + 2 < 4 32) 3 2 + 5 = 45 33) 2 + 7 4 > 6 Absolute value is a DISTANCE.

24 27) = 9 28) + 5 > 7 29) 5ℎ + 2 = 8 30) ) < 4 32) = 45 33) > 6 Absolute value is a DISTANCE. Distances cannot be negative Go back and check your work to make sure you didn t get a solution when the ABSOLUTE VALUE was equal to a negative number

25 Write an absolute value equation or absolute value inequality for each graph. 34) 35) 36) 37) Solve each real world problem. 38) Tina uses the elliptical machine at the gym. Her general goal is to burn 280 calories per workout, but she varies by as much as 25 calories from this amount on any given day. 39) Tim s bowling score was within 5 points of his average score of 120. A) What is the range of scores for Tim s game? A) Write an absolute value equation to find the maximum and minimum calories Tina burns on the elliptical machine. B) Graph this range. B) Solve. C) Write the absolute value inequality that describes this situation.

Chapter 5: Linear Inequalities

Chapter 5: Linear Inequalities Lesson 5-1: Solving Inequalities by Addition and Subtraction An is a statement that contains ,, or. notation is a way of writing a solution set. Example 1: Solve each inequality. Check your solution.