Main Idea Key Concept Addition and Subtraction Properties

Main Idea Key Concept: Addition and Subtraction Properties of Inequality Example 1: Solve Inequalities Using Subtraction and Addition Example 2: Solve Inequalities Using Subtraction and Addition Example 3: Graph Solutions of Inequalities Example 4: Write an Inequality

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

Solve Inequalities Using Subtraction and Addition Solve x + 5 > 12 x + 5 – 5 > 12 – 5 x >7 Write the inequality. Subtract 5 from each side. Simplify. Answer: The solution is x > 7.

Solve x – 5 < 10. A. x < 5 B. x > 5 C. x < 15 D. x > 15

Solve Inequalities Using Subtraction and Addition Solve – 8 ≥ y + 3 Write the inequality. – 8 – 3 ≥ y + 3 – 3 Subtract 3 from each side. – 11 Simplify. ≥y Answer: The solution is – 11 ≥ y or y ≤ – 11.

Solve 4 ≥ h + 1. A. 5 ≥ h B. 5 ≤ h C. 3 ≥ h D. 3 ≤ h

Graph Solutions of Inequalities Solve . Graph the solution set on a number line. Write the inequality. Subtract of 4. from each side. Rename 2 as a fraction with a denominator Simplify.

Graph Solutions of Inequalities The solution is Graph the solution. .

Graph Solutions of Inequalities Answer: The solution is .

Solve d + line. A. B. C. D. < 6. Graph the solution set on a number

Write an Inequality SHOPPING Jerome took $20 to the store to buy a book and some CDs. If he buys a book that costs $4. 50, what is the most he could spend on CDs? We need to find the greatest amount of money Jerome can spend on CDs. Let y represent the amount Jerome can spend on CDs. Write an inequality to represent the problem. .

Write an Inequality 4. 5 + y 20 4. 5 – 4. 5 + y 20 – 4. 5 y 15. 5 Write the inequality. (4. 50 = 4. 5) Subtract 4. 5 from each side. Simplify. Check by choosing an amount less than or equal to $15. 50, such as $10. Then Jerome would spend $4. 50 + $10 or $14. 50 in all. Since $14. 50 < $20, the answer is reasonable. Answer: So, the most Jerome can spend on CDs is $15. 50.

BOWLING Monique took $15 to the bowling alley. Shoe rental costs $3. 75. What is the most she could spend on games and snacks? A. x < $12. 25 B. x ≤ $11. 25 C. x < $11. 25 D. x > $11. 25