1. EXAMPLE 1 Solving and Graphing a Two-Step Inequality 10 + 4y < 18 Original inequality 10 + 4y – 10 < 18 – 10 Subtract 10 from each side. 4y < 8 Simplify. 4y 4 < 8 4 Divide each side by 4. y < 2 Simplify. Use an open circle and draw the arrow to the left.

2. EXAMPLE 2 Combining Like Terms 3x – 8 < – x + 4 Original inequality 3x – 8 – 3x < – x + 4 – 3x Subtract 3x from each side. – 8 < – 4x + 4 Combine like terms. – 8 – 4 < – 4x + 4 – 4 Subtract 4 from each side. – 12 < – 4x Simplify. –12 – 4 > –4x – 4 Divide each side by – 4 and reverse the inequality symbol. 3 > x Simplify.

3. EXAMPLE 3 Writing and Solving a Multi-Step Inequality Charity Bowling You are organizing a bowling night for charity. Each ticket costs $10 and includes shoe rental. Shoe rental costs you $5 per pair, and door prizes cost you $50. What are the possible numbers of people who need to attend for you to make a profit of at least $200 ? SOLUTION To find the amount you can raise, subtract the total costs from the total ticket sales. Let x represent the number of people.

4. EXAMPLE 3 Writing and Solving a Multi-Step Inequality 10x – (5x + 50) ≥ 200 Write an inequality. 10x – 5x – 50 ≥ 200 Distributive property 5x – 50 ≥ 200 Combine like terms. 5x ≥ 250 Add 50 to each side. x ≥ 50 Divide each side by 5. ANSWER At least 50 people need to attend the bowling night.

5. GUIDED PRACTICE for Examples 1, 2 and 3. Solve the inequality. Then graph the solution. z ≤ –6 –7z + 15 ≥ 57 1.

6. GUIDED PRACTICE for Examples 1, 2 and 3. n < – 5 11n + 36 < 3n – 4 2.

7. GUIDED PRACTICE for Examples 1, 2 and 3. 9(y – 2) > –16 3. y > 2 9

8. GUIDED PRACTICE for Examples 1, 2 and 3. 4. What If? In Example 3, suppose that each ticket also includes a $1 beverage. How many people need to attend for you to make a profit of at least $200 ? ANSWER At least 63 people need to attend the bowling night.