• Solve inequalities by using the Addition or Subtraction Properties of Inequality.

Solving Inequalities

Solve –21 ≥ d – 8. Check your solution.

–21 ≥ d – 8 Write the inequality.

–21 + 8 ≥ d – 8 + 8 Add 8 to each side.

–13 ≥ d or d ≤ –13Simplify.

Answer: The solution is –13 ≥ d or d ≤ –13.

Check

–21 ≥ d – 8 Write the inequality.

–21 ≥ –22 This statement is true.

–21 ≥ –14 – 8Replace d with a number less than or equal to –13, such as –14.

?

1. A

2. B

3. C

4. D0% 0%0%0%

A. b > 16

B. b > 8

C. b > –8

D. b > –16

Solve b – 12 > 4.

Solving Inequalities

Solve y + 5 > 11. Check your solution.

y + 5 > 11 Write the inequality.

y + 5 – 5 > 11 – 5 Subtract 5 from each side.

y > 6 Simplify.

Answer: The solution is y > 6.

Check Replace y in the original inequality with a number greater than 6.

1. A

2. B

3. C

4. D0% 0%0%0%

A. g ≤ 4

B. g ≥ 4

C. g ≤ –4

D. g ≥ –4

Solve 9 ≤ g + 13. Check your solution.

Kayta took $12 to the bowling alley. Shoe rental costs $3.75. What is the most he could spend on games and snacks?

Read the ItemThe phrase the most means less than or equal to.

Solve the ItemLet d = dollars spent on games and snacks.

Estimate $12 – $4 = $8

Cost of shoe rental plus

dollars spent on games and snacks

is less than or equal to $12.

3.75 d 12

3.75 + d ≤12 Write the inequality.

Answer: So, Kayta could spend no more than $8.25 on games and snacks.

3.75 – 3.75 + d ≤12 – 3.75

Subtract 3.75 from each side.

d ≤ 8.25Simplify.

Check for Reasonableness $8.25 ≈ $8

1. A

2. B

3. C

4. D0% 0%0%0%

A. $17.00

B. $17.70

C. $17.75

D. $18.75

Monique took $20 to the bookstore. She spent $2.25 on a snack at the library café. What is the most she could spend on books?

1. A

2. B

3. C

4. D0% 0%0%0%

A. g > 90

B. g ≥ 90

C. g < 90

D. g ≤ 90

Write an inequality for the sentence. A grade of no less than 90 is considered an "A."

(over Lesson 8-6)

1. A

2. B

3. C

4. D0% 0%0%0%

A. a ≥ 10

B. a > 10

C. a ≤ 10

D. a < 10

Write an inequality for the sentence. Children age 10 and under can order from the kids menu.

(over Lesson 8-6)

1. A

2. B

0%0%

A. true

B. false

For the given value, state whether the inequality is true or false.8 + n > 12; n = 5

(over Lesson 8-6)

1. A

2. B

0%0%

A. true

B. false

For the given value, state whether the inequality is true or false.y – 15 ≤ –7; y = 8

(over Lesson 8-6)

1. A

2. B

0%0%

A. true

B. false

For the given value, state whether the inequality is true or false.–5x ≤ 40; x = –10

(over Lesson 8-6)

1. A

2. B

3. C

4. D

0% 0%0%0%

A. n > 5

B. n ≥ 5

C. n < 5

D. n ≤ 5

Which inequality is graphed on the number line?

(over Lesson 8-6)