Key Concept: Addition and Subtraction Properties of Inequality 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 Lesson Menu

Solve inequalities by using the Addition and Subtraction Properties of Inequality. Main Idea/Vocabulary

Key Concept

Solve Inequalities Using Subtraction and Addition Solve x + 5 > 12. x + 5 > 12 Write the inequality. x + 5 – 5 > 12 – 5 Subtract 5 from each side. x > 7 Simplify. Answer: The solution is x > 7. Example 1

Solve x – 5 < 10. A. x < 5 B. x > 5 C. x < 15 D. x > 15 Example 1 CYP

Solve Inequalities Using Subtraction and Addition Solve –8 ≥ y + 3. –8 ≥ y + 3 Write the inequality. –8 – 3 ≥ y + 3 – 3 Subtract 3 from each side. –11 ≥ y Simplify. Answer: The solution is –11 ≥ y or y ≤ –11. Example 2

Solve 4 ≥ h + 1. A. 5 ≥ h B. 5 ≤ h C. 3 ≥ h D. 3 ≤ h Example 2 CYP

Graph Solutions of Inequalities Solve . Graph the solution set on a number line. Write the inequality. Subtract from each side. Rename 2 as a fraction with a denominator of 4. Simplify. Example 3

Graph Solutions of Inequalities The solution is . Graph the solution. Example 3

Graph Solutions of Inequalities Answer: The solution is . Example 3

Solve d + < 6. Graph the solution set on a number line. C. D. Example 3 CYP

We need to find the greatest amount of money Jerome can spend on CDs. 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. . Example 4

4.5 + y  20 Write the inequality. (4.50 = 4.5) Write an Inequality 4.5 + y  20 Write the inequality. (4.50 = 4.5) 4.5 – 4.5 + y  20 – 4.5 Subtract 4.5 from each side. y  15.5 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. Example 4

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 Example 4 CYP