2. Lesson Menu Main Idea Example 1:Solve Multi-Step Inequalities Example 2:Solve Multi-Step Inequalities

3. Main Idea/Vocabulary Use properties of inequality to solve multi-step inequalities.

4. Example 1 Solve Multi-Step Inequalities Solve –4d + 2(d + 5) > 12. Graph the solution set on a number line. –4d + 2(d + 5) > 12Write the equation. –4d + 2d + 10 > 12Distributive Property –2d + 10 > 12Simplify. – 10 >– 10Subtraction Property of Inequality –2d > 2Simplify. d <–1Simplify. Division Property of Inequality; reverse inequality symbol.

5. Example 1 Graph the solution set on a number line. Use an open dot because –1 is not included. Solve Multi-Step Inequalities Answer: d < –1;

6. Example 1 CYP 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; __ 3 4

7. Example 2 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

8. Example 2 Solve Multi-Step Inequalities 3(d + 35) + 70 ≤ 550Write the equation. 3d + 105 + 70 ≤ 550Distributive Property 3d + 175 ≤ 550Simplify. – 175 – 175Subtraction Property of Inequality 3d ≤ 375Simplify. d ≤ 125Simplify. Division Property of Inequality Answer:So, the maximum Rami can spend for painting a room is $125.

9. Example 2 CYP 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.