Practice A. Solving Inequalities by Adding or Subtracting. Solve. Then match each solution set with its graph. 1. r 1 2 A. 2. m 3 6 B. 3. x 4 1 C.

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1 Practice A Solving Inequalities by Adding or Subtracting Solve. Then match each solution set with its graph. 1. r 1 2 A. 2. m 3 6 B. 3. x 4 1 C. 4. k 2 5 D. Solve. Check each answer. 5. a h v y 7 9. j t w f b Friday s high temperature was 20 F. Saturday s high temperature was forecast to be no more than 8 F warmer than Friday s high temperature. According to the forecast, what are the possible high temperatures for Saturday?

2 Practice B Solving Inequalities by Adding or Subtracting Solve. Then graph each solution set on a number line. 1. y n x h p s 7 16 Solve. Check each answer g w a z t b In order for a field trip to be scheduled, at least 30 students must sign up. So far, 23 students have signed up. At least how many more students must sign up in order for the field trip to be scheduled?

3 Practice C Solving Inequalities by Adding or Subtracting Solve. Then graph each solution set on a number line. 1. a ( 5) 2 2. m x Solve. Check each answer. 4. j w 9 ( 1) 3 6. r k x ( 13) 18 8 ( 9) b t s z n Nine members of the drama club are going to New York to see a Broadway play as a group. The total cost for the tickets, including a $15.00 handling fee, will be no more than $ What is the maximum cost of each ticket?

4 Review for Mastery Solving Inequalities by Adding or Subtracting Inequalities with variables may have more than one solution. All the solutions of an inequality are called the solution set. You can solve an inequality involving addition or subtraction just as you would solve an equation. Complete the steps to solve, graph, and check the inequality. 1. n x 18 2 n 13 7 x 18 2 n x Graph the inequality. Graph the inequality. Check: Check: Pick any number in the solution set Pick any number in the solution set of of n 20. of x Substitute 19 into the inequality. n 13 7 Substitute 0 into the inequality. x ? 7 18? 2? 7? 2 Solve. Then graph each solution set. 3. d s 10 6 Solve. Check each answer. 5. y h a 4 18

5 Challenge Absolute Value Equations The absolute value of a number x is: x x if x 0 and x x if x 0 When you solve an absolute value equation, you must consider both of these cases. Example: Solve n Case 1: n 8 20 Case 2: (n 8) 20 n 12 n 8 20 n 28 n 28 The equation has two solutions: n 12, 28 Solve. 1. t s y g m p c n e x k s w b r 1 17

6 Problem Solving Solving Inequalities by Adding or Subtracting Write the correct answer. 1. A small car averages up to 29 more miles per gallon of gas than an SUV. If a small car averages 44 miles per gallon, what is the average miles per gallon for an SUV? 2. Carlos is taking a car trip that is more than 240 miles, depending on the route he chooses. He has already driven 135 miles. How much farther does he have to go? 3. Driving into the city usually takes 25 minutes. If there is a lot of traffic, the trip can take up to 45 minutes. How much additional time should you allow during a heavy traffic period? Choose the letter for the best answer. 5. On one day, the range of temperatures in one state was at most 27. If the lowest temperature in the state was 59, what was the highest temperature? A t 86 C t 86 B t 86 D t Romero is saving to buy an Apex Model 12 Computer. The lowest price that Romero can find for the computer is $1,250. Romero now has $825. His grandmother is going to give him another $200. How much more money does Romero need? A x $225 C x $225 B x < $425 D x $ To qualify for the heavyweight wrestling division, Kobe must weigh at least 180 pounds. If Kobe weighs 168 pounds now, how much weight should he gain? 6. The highest possible score on the Scholastic Aptitude Test is 2,400. Rebecca scored 1,780. She needs a score of at least 1,950 to qualify for a scholarship. How much higher must her score be? F s 170 H s 170 G s 450 J s The seating capacity of the school gym is 550. So far, there are 210 fans at a basketball game. How many more fans could attend the game? F f 340 G f 210 H f 340 J f 340

7 Reading Strategies Use a Graphic Organizer You can use this chart to help you understand solving two-step inequalities. Solution of the Inequality Any value of the variable that makes the inequality true. Addition Inequality x 4 25 x x 21 Solving Inequalities by Adding or Subtracting Solution Set All possible solutions of an inequality. Subtraction Inequality y 8 12 y y 20 Use the graphic organizer to answer the following questions. 1. What is a solution of an inequality? 2. What is the solution set? 3. What are 3 solutions for x 21? 4. What are 3 solutions for y 20? 5. Why is x 4 25 called an Addition Inequality?

8 Across Puzzles, Twisters & Teasers Are All Puzzles Created Equal? 1. You can use an to solve a problem. 4. Inequalities with usually have many solutions. 5. Any value of a variable that makes a true is a solution of the inequality. 7. When your solution, you should choose a number in the solution set that is easy to work with. 9. All of the solutions of an inequality are called the set. Down 2. You can find solution sets for inequalities by the variable. 3. You can check your answer by choosing any number in the solution set and it into the original inequality. 6. You can solve one- inequalities by adding or subtracting. 8. When you add or the same number to both sides of an inequality, the statement will still be true.

9 LESSON 12-5 Practice A 1. r 3 A. 2. m 3 B. 3. x 3 C. 4. k 3 D. 5. a 5 6. h v 8 8. y j t w t b The possible high temperature is at most 28 F. Practice B 1. y 3 2. n t b 13. At least 7 more students must sign up. Practice C 1. a 3 2. m 1 3. x 3 4. j w r k x b t s z n 5 6 Review for Mastery 1. 13; 13; 20 Check: 19; ; 18; $ x 5 4. h 18 Check: 0; d 8 5. p s 4 6. s 9 7. g w a z y h a 14 Challenge 1. t 5, s 12, y 4, 4 4. g 9, 3

10 5. m 11, p 7 2, 4 Puzzles, Twisters & Teasers 7. c 20, 6 8. n 7 3, 5 9. e 16, x 8, k 5, s 7, w 1 3, b 3 2, r 8 3, 3 Problem Solving 1. at least 15 mi per gal 2. more than 105 miles 3. no more than 20 min 4. at least 12 lb 5. B 6. H 7. C 8. H Reading Strategies 1. any value for the variable that makes the inequality true 2. all the possible solutions of an inequality 3. possible answers: 22, 23, possible answers: 19, 18, is added to the variable x in the inequality.