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

Main Idea/Vocabulary

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KC 1

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

Solving Inequalities Solve –21 ≥ d – 8. Check your solution. –21 ≥ d – 8 Write the inequality. – ≥ d – Add 8 to each side. –13 ≥ d or d ≤ –13 Simplify. Check –21 ≥ d – 8 Write the inequality. –21 ≥ –14 – 8 Replace d with a number less than or equal to –13, such as –14. ? –21 ≥ –22 This statement is true. Answer: The solution is –13 ≥ d or d ≤ –13. Example 1

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**Solve b – 12 > 4. A. b > 16 B. b > 8 C. b > –8**

D. b > –16 A B C D Example 1

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**Solve y + 5 > 11. Check your solution.**

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. Check Replace y in the original inequality with a number greater than 6. Answer: The solution is y > 6. Example 2

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**Solve 9 ≤ g + 13. Check your solution.**

A. g ≤ 4 B. g ≥ 4 C. g ≤ –4 D. g ≥ –4 A B C D Example 2

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**dollars spent on games and snacks**

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 Item The phrase the most means less than or equal to. Solve the Item Let 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 Example 3

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**3.75 + d ≤ 12 Write the inequality.**

3.75 – d ≤ 12 – 3.75 Subtract 3.75 from each side. d ≤ 8.25 Simplify. Check for Reasonableness $8.25 ≈ $8 Answer: So, Kayta could spend no more than $8.25 on games and snacks. Example 3

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**Monique took $20 to the bookstore. She spent $2**

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? A. $17.00 B. $17.70 C. $17.75 D. $18.75 A B C D Example 3

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(over Lesson 8-6) Write an inequality for the sentence. A grade of no less than 90 is considered an "A." A. g > 90 B. g ≥ 90 C. g < 90 D. g ≤ 90 A B C D Five Minute Check 1

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(over Lesson 8-6) Write an inequality for the sentence. Children age 10 and under can order from the kids menu. A. a ≥ 10 B. a > 10 C. a ≤ 10 D. a < 10 A B C D Five Minute Check 2

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(over Lesson 8-6) For the given value, state whether the inequality is true or false. 8 + n > 12; n = 5 A. true B. false A B Five Minute Check 3

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(over Lesson 8-6) For the given value, state whether the inequality is true or false. y – 15 ≤ –7; y = 8 A. true B. false A B Five Minute Check 4

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(over Lesson 8-6) For the given value, state whether the inequality is true or false. –5x ≤ 40; x = –10 A. true B. false A B Five Minute Check 5

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**Which inequality is graphed on the number line?**

(over Lesson 8-6) Which inequality is graphed on the number line? A. n > 5 B. n ≥ 5 C. n < 5 D. n ≤ 5 A B C D Five Minute Check 6

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