• Solve inequalities by using the Multiplication or Division Properties of Inequality.

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

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 6.6 6

1. A

2. B

3. C

4. D0% 0%0%0%

A. x < –6

B. x < 6

C. x > –6

D. x > 6

Solve 4x < –24.

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.

1. A

2. B

3. C

4. D0% 0%0%0%

A. p < 10

B. p > –10

C. p > 10

D. p > 7

> 5.

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

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.

1. A

2. B

3. C

4. D0% 0%0%0%

A. x ≥ 21

B. x ≥ –21

C. x ≤ 21

D. x ≤ –21

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.

4 4

1. A

2. B

3. C

4. D0% 0%0%0%

A. b > 7

B. b > –7

C. b < 7

D. b < –7

Solve –8b < –56.

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

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 – 1 Subtract 1 from each side.

Divide each side by 2.

Simplify.

2 2

1. A

2. B

3. C

4. D0% 0%0%0%

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?

1. A

2. B

3. C

4. D0% 0%0%0%

A. y < 5

B. y < –5

C. y < 11

D. y > –11

Solve y – 8 < –3. Check your solution.

(over Lesson 8-7)

1. A

2. B

3. C

4. D0% 0%0%0%

A. g ≥ 1

B. g ≤ –13

C. g ≥ –13

D. g ≤ 1

Solve –6 ≤ 7 + g. Check your solution.

(over Lesson 8-7)

1. A

2. B

3. C

4. D0% 0%0%0%

A. k ≥ 12

B. k ≥ –12

C. k ≤ –6

D. k ≥ –6

Solve k + 9 ≥ 3. Check your solution.

(over Lesson 8-7)

1. A

2. B

3. C

4. D0% 0%0%0%

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)

1. A

2. B

3. C

4. D0% 0%0%0%

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)

1. A

2. B

3. C

4. D

0% 0%0%0%

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)