Pre Alg TE Lesson 2-9

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2 EXAMPLE Real-World Problem Solving 2. Teach Computers Nearly 32 megabytes (MB) of memory are available for running your computer. If its basic systems require 12 MB, how much memory is available for other programs? Words memory for plus memory for is less basic systems other programs than Let m = memory available for other programs. Inequality 12 + m , 32 12 + m , 32 12 - 12 + m , 32 - 12 Subtract 12 from each side. m , 20 Simplify. Less than 20 MB of memory is available for other programs. Check Understanding Example 2 2. An airline lets you check up to 65 lb of luggage. One suitcase weighs 37 lb. How much can another suitcase weigh? K 28 lb OBJECTIVE 3 2 Using Addition to Solve Inequalities To solve an inequality involving subtraction, use addition. Key Concepts Addition Property of Inequality You can add the same number to each side of an inequality. Arithmetic 7 . 3, so 7 + 4 . 3 + 4 2 , 5, so 2 + 6 , 5 + 6 EXAMPLE Solve n – 15 R 3. n - 15 , 3 n - 15 + 15 , 3 + 15 n , 18 Check Understanding Example 3 3. Solve each inequality. Algebra If a . b, then a + c . b + c. If a , b, then a + c , b + c. Adding to Solve an Inequality Add 15 to each side. Simplify. a. m - 13 . 29 b. v - 4 # 7 c. t - 5 $ 11 m S 42 v K 11 t L 16 total memory 1 A B C D E 2 A B C D E 3 A B C D E 4 A B C D E 5 A B C D E B C D E Test-Taking Tip To check that n , 18 is a solution of n - 15 , 3, use related equations n = 18 and n - 15 = 3. Substitute 18 into n - 15 = 3 and get 18 - 15 = 3. The result suggests that you solved correctly. 2-9 Solving One-Step Inequalities by Adding or Subtracting 107 Math Background The same number can be added to or subtracted from each side of an inequality to get a new inequality with the same solutions as the original. Teaching Notes 1 Error Prevention Point out that to rewrite an inequality in reverse order, you must pay attention to the direction of the inequality symbol. You rewrite 5 . x as x , 5, changing . to ,. Have students write an inequality for Kyle is older than Jaime in two ways. Kyle’s age > Jaime’s age; Jaime’s age < Kyle’s age 2 Diversity Some students may be unfamiliar with computer terminology. Explain that a byte is a unit of computer memory that stores a single character. Explain to students that the prefix mega means one million. Ask students to guess what 1 megabyte might mean. one million bytes 1 2 3 EXAMPLE EXAMPLE PowerPoint Additional Examples Solve each inequality. Graph the solutions. a. 4 + s , 12 s R 8 b. -16 $ y - 14 –2 L y or y K–2 See back of book for graphs. Suppose your computer’s hard drive has a capacity of 6 gigabytes (GB). The files you have stored on the hard drive occupy at least 2 GB. How much storage space is left for other files? s K 4; at most 4 GB are left. Solve -10 , -13 + q. 3 R q Reaching All Students Closure Below Level Ask: What do you do to each side of the equation to get the variable alone for d + 5 = 9? Subtract 5. For f - 6 = 4? Add 6. Advanced Learners Ask: If you try to list all the solutions for x > 1, which number would you list first? Explain. Answers may vary. Sample: 2; because it’s the first integer greater than 1. Error Prevention See note on page 107. Diversity See note on page 107. Ask students to compare solving inequalities involving addition and subtraction with solving equations involving addition and subtraction. See back of book. 107
3. Practice Assignment Guide 1 Objective 1 A B Core 1–10, 20, 23, 28, 29, 31–34 C Extension 35, 37 2 Objective 2 A B Core 11–19, 21, 22, 24–27, 30 C Extension 36 Test Prep 38–40 Mixed Review 41–47 108 Practice 2-9 Solving One-Step Inequalities by Adding or Subtracting Write an inequality for each sentence. Then solve the inequality. 1. Six less than n is less than 4. n 2 6 * 4; n * 2 2. The sum of a number k and five is greater than or equal to two. k 1 5 # 2; k # 3 3. Nine more than a number b is greater than negative three. b 1 9 + 3; b + 12 4. You must be at least 48 inches tall to ride an amusement park ride, and your little sister is 39 inches tall. How many inches i must she grow before she may ride the ride? 39 1 i # 48; i # 9 5. You need no more than 3,000 calories in a day. You consumed 840 calories at breakfast and 1,150 calories at lunch. How many calories c can you eat for dinner? 840 1 1,150 1 c " 3,000; c " 1,010 Solve each inequality. Graph the solutions. 6. 7 1 x $ 9 x # 2 7. 25 # x 2 6 5 4 3 2 1 8. 0 $ x 1 12 x " 12 9. 16 12 8 10. 13 1 x $ 13 x # 0 11. 5 4 3 2 1 12. 4 1 x ,22 x * 6 13. 8 7 6 5 4 14. x 2 6 #21 x " 5 15. 5 4 3 2 1 0 1 2 3 4 5 4 0 4 0 1 2 3 4 5 3 21 0 1 2 0 1 2 3 4 5 5 4 3 2 1 x 2 15 #28 2 1 0 x 2 8 .25 5 4 3 2 1 x 2 9 .211 1 2 5 4 3 2 1 24 1 x ,24 5 4 3 2 1 x # 1 0 1 2 3 4 5 x " 7 3 4 5 6 7 8 x + 3 0 1 2 3 4 5 x + 2 0 1 2 3 4 5 x * 0 0 1 2 3 4 5 Solve each inequality. Then write the letter matching the solution in the key on the line to the left of the problem number. The result will be something fun to do. H 1. x 1 2 , 13 x * 11 Key A 2. x " 4 A x #24 x 2 1 #25 D x , 3 V 3. 15 , x 1 17 x + 2 E x . 3 H x , 11 E 4. x 2 9 .26 x + 3 I x $ 9 M x # 9 N x ,23 P x $ 2 A 5. 26 $ x 2 2 x " 4 R x , 5 S x $24 T x $25 P 6. x 2 12 $210 x # 2 U x . 1 V x .22 I 7. x 2 5 $ 4 x # 9 Y x #22 Z 8. x 1 2 . 6 x + 4 Z x . 4 Z 9. 25 , x 2 9 x + 4 A 10. 3 $ x 1 7 x " 4 P A R T Y Enrichment 2-9 11. 26 # x 2 8 x # 2 12. x 1 8 # 4 x " 4 13. 2 1 x , 7 x * 5 14. 4 # x 1 9 x # 5 15. 25 $ x 2 3 x " 2 Having Fun Practice Enrichment EXERCISES Practice and Problem Solving A B Practice by Example Example 1 (page 106) Example 2 (page 107) Example 3 (page 107) Apply Your Skills 35. Comm. Prop. of Add. Simplify. Subt. Prop. of Inequality Simplify. 36. Subt. within parentheses. Simplify. Add. Prop. of Inequality Simplify. C Challenge 108 Chapter 2 Solving One-Step Equations and Inequalities GPS 22. Use the Guided Problem Solving worksheet with Exercise 10. 0 2 6 Solve each inequality. Graph the solutions. 1–8. See back of book for graphs. 1. w + 5 , 12 2. 2 . 9 + a 3. x + 6 $ 7 4. 2 + m # 2 w R 7 a R–7 x L 1 m K 0 5. 18 # 20 + w 6. -7 , 5 + x 7. 30 $ t + 45 8. p + 22 $ -10 w L–2 x S–12 t K–15 p L–32 9. Transportation The total weight limit for a truck is 100,000 lb. The truck weighs 36,000 lb empty. What is the most that the truck’s load can weigh? 64,000 lb 10. Budgeting You are saving to buy a bicycle that will cost at least GPS $120. Your parents give you $45 toward the bicycle. How much money will you have to save? L $75 Solve each inequality. 11. x - 5 $ 6 12. n - 12 # 3 13. r - 4 # 3 x L 11 n K 15 r K 7 14. x - 7 , 15 15. c - 9 . 5 16. h - 10 $ 6 x R 22 c S 14 h L 16 17. w - 8 , 3 18. 12 $ y - 5 19. 4 $ y - 4 w R 11 y K 17 y K 8 What do you do to the first inequality to get the second inequality? 20. x + 8 # 11; x # 3 21. x - 3 . 9; x . 12 Subtract 8 from each side. Add 3 to each side. Solve each inequality. Graph the solutions. 22–30. See margin for graphs. 22. x - 8 . -2 23. 6 , y + 19 24. 3 # y - 5 x S 6 y S–13 y L 8 25. -8 $ k - 3 26. -3 + y . 4 27. a - 0.5 , 2.5 k K–5 y S 7 a R 3 28. 7 + r . 11 29. 9 , b + 4 30. u - 3 $ 9 r S 4 b S 5 u L 12 Write an inequality for each sentence. Then solve the inequality. 31. Thirteen plus a number 32. The sum of a number w and n is greater than fifteen. 3 is less than or equal to ten. 13 ± n S 15; n S 2 w ± 3 K 10; w K 7 33. Shopping Jim has $87. He spends $6 for socks and at least $32 for shoes. How much does he have left to spend for shirts? K $49 34. A store’s dressing room has a limit of 10 garments per customer. If Carol has at least 3 garments below the limit, how many garments does she have in her dressing room? K 7 garments Reasoning Justify each step. 35–36. See above left. For more exercises, see Extra Practice. 35. 4 + a + 3 . 16 36. m - 2(8 - 5) # -9 4 + 3 + a . 16 m - 2(3) # -9 7 + a . 16 m - 6 # -9 7 - 7 + a . 16 - 7 m - 6 + 6 # -9 + 6 a . 9 m # -3 23. 13 0 5 24. 0 2 8 25–30. See back of book.
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