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Main Idea/Vocabulary Solve inequalities by using the Multiplication or Division Properties of Inequality.

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KC 1 These properties are also true for a ≥ b and a ≤ b.

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Example 1 Solve Inequalities by Dividing Solve 6x < –30. Check your solution. Answer: The solution is x < –5. You can check this solution by substituting numbers less than –5 into the inequality. Write the inequality. Simplify. Divide each side by 6. 66

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1.A 2.B 3.C 4.D Example 1 A.x < –6 B.x < 6 C.x > –6 D.x > 6 Solve 4x < –24.

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Example 2 Solve Inequalities by Multiplying Write the inequality. Answer: The solution is p ≥ 18. You can check this solution by substituting 18 and a number greater than 18 into the inequality. Multiply each side by 2. Simplify.

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1.A 2.B 3.C 4.D Example 2 A.p < 10 B.p > –10 C.p > 10 D.p > 7 > 5.

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KC 2 These properties are also true for a ≥ b and a ≤ b.

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Example 3 Multiply or Divide by a Negative Number Answer: The solution is b ≥ –20. You can check this solution by replacing b in the original inequality with –20 and a number greater than –20. Write the inequality. Simplify. Multiply each side by –4 and reverse the inequality symbol.

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1.A 2.B 3.C 4.D Example 3 A.x ≥ 21 B.x ≥ –21 C.x ≤ 21 D.x ≤ –21

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Example 4 Solve –4n > –60. Check your solution. Answer: The solution is n < 15. Multiply or Divide by a Negative Number Write the inequality. Check this result. Divide each side by –4 and reverse the inequality symbol. 44

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1.A 2.B 3.C 4.D Example 4 A.b > 7 B.b > –7 C.b < 7 D.b < –7 Solve –8b < –56.

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Example 5 PACKAGES A box weighs 1 pound. It is filled with books that weigh 2 pounds each. Jesse can carry at most 20 pounds. Assuming space is not an issue, write and solve an inequality to find how many books he can put in the box and still carry it. The phrase at most means less than or equal to. Let p = the number of books he puts in the box. Then write an inequality. 1 pound plus 2 pounds per book is less than or equal to 20 pounds. 1 2p 20

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Example 5 Answer: Since he can not put half a book in the box, Jesse can put at most 9 books in the box. Write the inequality. Simplify. 1 – 1 + 2p ≤ 20 – 1Subtract 1 from each side. Divide each side by 2. Simplify. 22

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1.A 2.B 3.C 4.D Example 5 A.18 toys B.24 toys C.28 toys D.30 toys PACKAGES A box weighs 2 pounds. It is filled with toys that weigh 1 pound each. Danielle can carry at most 30 pounds. Assuming space is not an issue, how many toys can she can put in the box and still carry it?

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1.A 2.B 3.C 4.D Five Minute Check 1 A.y < 5 B.y < –5 C.y < 11 D.y > –11 Solve y – 8 < –3. Check your solution. (over Lesson 8-7)

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1.A 2.B 3.C 4.D Five Minute Check 2 A.g ≥ 1 B.g ≤ –13 C.g ≥ –13 D.g ≤ 1 Solve –6 ≤ 7 + g. Check your solution. (over Lesson 8-7)

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1.A 2.B 3.C 4.D Five Minute Check 3 A.k ≥ 12 B.k ≥ –12 C.k ≤ –6 D.k ≥ –6 Solve k + 9 ≥ 3. Check your solution. (over Lesson 8-7)

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1.A 2.B 3.C 4.D Five Minute Check 4 A.n – 7 > 16; n > 23 B.n + 7 ≤ 16; n ≤ 9 C.n + 7 ≥ 16; n ≥ 9 D.n + 16 ≥ 7; n ≥ –9 Write an inequality and solve the problem. Seven more than a number is at least 16. (over Lesson 8-7)

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1.A 2.B 3.C 4.D Five Minute Check 5 A.n – 5 > –11; n > –6 B.n – 5 < –11; n < –6 C.n + (–11) > 5; n > 16 D.n + 5 ≤ –11; n ≤ –16 Write an inequality and solve the problem. The difference between a number and 5 is less than –11. (over Lesson 8-7)

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1.A 2.B 3.C 4.D Five Minute Check 6 A.12 ≥ 5 + d B.12 > 5 + d C.12 < 5 + d D.12 ≤ 5 + d Marcus jogs at least 5 more miles per week than his dad. Marcus jogs 12 miles per week. Which inequality can be used to determine how many miles Marcus’ dad jogs per week? (over Lesson 8-7)

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