1. Example 1 Solving and Graphing a Two-Step Inequality 4y4y+10 < 18 Original inequality 4y4y < 8 Simplify. < –– Subtract 10 from each side. 18 10 4y4y+ (Subtraction property of inequality) 4 8 4 4y4y < Divide each side by 4. (Division property of inequality) < y2 Simplify. 012345

2. Example 2 Combining Like Terms Original inequality 143x3x < – x – Subtract 3x from each side. < 3x3x – 3x3x – (Subtraction property of inequality) 143x3x – x – Combine like terms. < 14 – 4x4x – Divide each side by and reverse the inequality symbol. (Division property of inequality) > 4 – 4x4x – 14 – 4 – 4 – Simplify. x 2 7 > 012345

3. Example 3 Multiple Choice Practice You are organizing a bowling night for charity. Each ticket costs $10 and includes shoe rental. Door prizes cost you $50. Which inequality describes the possible numbers x of people who need to attend for you to make a profit of at least $200 ? SOLUTION To find your profit, subtract the total costs from the total ticket sales. This amount should equal or exceed the minimum desired profit of $200. 15x ≤ x ≥ 25x ≤ x ≥

4. Example 3 Multiple Choice Practice ANSWER The correct answer is D. 5010x – 200 ≥ Write an inequality. Add 50 to each side. 250 ≥ 10x Divide each side by 10. 25 ≥ x

5. Guided Practice Solve the inequality. Then graph the solution. for Examples 1, 2, and 3 1. 157z7z + – ≥ 57 2. 4011n + 3n3n < ANSWER z 6 – ≤ n 5 – <

6. Guided Practice for Examples 1, 2, and 3 Solve the inequality. Then graph the solution. 3. 189y9y – 16 – > ANSWER > y 9 2

7. Guided Practice for Examples 1, 2, and 3 4. WHAT IF? In Example 3, how many people need to attend for you to make a profit of at least $250 ? ANSWER x ≥ 30 people