Main Idea

Example 1: Solve Multi-Step Inequalities

Example 2: Solve Multi-Step Inequalities

• Use properties of inequality to solve multi-step inequalities.

Solve Multi-Step Inequalities

Solve –4d + 2(d + 5) > 12. Graph the solution set on a number line.

–4d + 2(d + 5) > 12 Write the equation.–4d + 2d + 10 > 12 Distributive Property

–2d + 10 > 12 Simplify.– 10 > – 10 Subtraction Property of Inequality

–2d > 2 Simplify.

d < –1 Simplify.

Division Property of Inequality;reverse inequality symbol.

Graph the solution set on a number line. Use an open dot because –1 is not included.

Solve Multi-Step Inequalities

Answer: d < –1;

Solve 3(n – 1) + 5n 5. Graph the solution set on a number line.

A. n ≥ –1;

B. n ≥ ;

C. n < 1;

D. n ≤ 1;

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PAINT Rami can spend $550 at most to have 3 rooms painted. A painter charges d dollars per room to paint and $35 per room for prep work. There is a one-time $70 charge for supplies. Write and solve an inequality to find the maximum Rami can spend for painting a room.

Solve Multi-Step Inequalities

Solve Multi-Step Inequalities

3(d + 35) + 70 ≤ 550 Write the equation.3d + 105 + 70 ≤ 550 Distributive Property

3d + 175 ≤ 550 Simplify.– 175    – 175 Subtraction Property of Inequality

3d ≤ 375 Simplify.

d ≤ 125 Simplify.

Division Property of Inequality

Answer: So, the maximum Rami can spend for painting a room is $125.

A. 4(12 + d) ≤ 80; d ≤ $8.00

B. 4(7 + d) + 5 ≤ 80; d ≤ $11.75

C. 4(5 + d) + 7 ≤ 80; d ≤ $13.25

D. 4d + 7 + 5 ≤ 80; d ≤ $17.00

FAIR A family of four can spend $80 at most at the fair. Parking costs $5 and each ticket costs $7. Each person is given d dollars to spend on food and drinks. Write and solve an inequality to find the maximum amount each person can spend on food and drinks.