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

4Divide each side by 4.

y < 2 Simplify.

Use an open circle and draw the arrow to the left.

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.

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.

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.

ANSWERAt least 50 people need to attend the bowling night.

GUIDED PRACTICE for Examples 1, 2 and 3.

Solve the inequality. Then graph the solution.

z ≤ –6

–7z + 15 ≥ 571.

GUIDED PRACTICE for Examples 1, 2 and 3.

n < – 5

11n + 36 < 3n – 42.

GUIDED PRACTICE for Examples 1, 2 and 3.

9(y – 2) > –16 3.

y > 29

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.