# Solving MultiStep Inequalities Warm Up Solve Check each

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Solving Multi-Step Inequalities Warm Up Solve. Check each answer. 1. 7 k < 42 2. 98 > – 14 n 3. 9 < 12 t 4. 21 g < 3 k<6 – 7 < n 3 4 <t g<1 7

Solving Multi-Step Inequalities Standards: MCC 7. EE. 4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Essential Question: How can you solve inequalities that involve one operation?

Solving Multi-Step Inequalities When you solve two-step equations, you can use the order of operations in reverse to isolate the variable. You can use the same process when solving multi-step inequalities.

Solving Multi-Step Inequalities Additional Example 1 A: Solving Two-Step Inequalities Solve. Then graph the solution set on a number line. y 2 – 6>1 +6 +6 Add 6 to both sides. y >7 2 y > (2)7 Multiply both sides by 2. (2) 2 y > 14 – 21 – 14 – 7 0 7 14 21

Solving Multi-Step Inequalities Additional Example 1 B: Solving Two-Step Inequalities Solve. Then graph the solution set on a number line. m 5≥ +8 – 3 – 8 Subtract 8 from both sides. m – 3 ≥ – 3 m Multiply both sides by – 3, and (– 3)(– 3) ≤ – 3 reverse the inequality symbol. m≥ 9 – 3 0 3 6 • 9 12 15

Solving Multi-Step Inequalities Check It Out: Example 1 A Solve. Then graph the solution set on a number line. h 7 + 1 > – 1 – 1 Subtract 1 from both sides. h > – 2 7 h > (7)(– 2) Multiply both sides by 7. (7) 7 h > – 14 – 21 – 14 – 7 0 7 14 21

Solving Multi-Step Inequalities Check It Out: Example 1 B Solve. Then graph the solution set on a number line. m +1≥ 7 – 2 – 1 Subtract 1 from both sides. m ≥ 6 – 2 (– 2) m ≤ (– 2)(6) Multiply both sides by – 2, and – 2 reverse the inequality symbol. m ≤ – 12 • – 18 – 12 – 6 0 6 12 18

Solving Multi-Step Inequalities WB: Pg. 160

Solving Multi-Step Inequalities Additional Example 2 A: Solving Multi-Step Inequalities Solve. Then graph the solution set on a number line. 6 y – 5 – 2 y < 11 4 y – 5 < 11 +5 +5 4 y < 16 4 4 y<4 – 6 – 4 – 2 0 Combine like terms. Add 5 to both sides. Divide both sides by 4. º 2 4 6

Solving Multi-Step Inequalities Additional Example 2 B: Solving Two-Step Inequalities Solve. Then graph the solution set on a number line. – 11 ≥ 2(– 3 x + 1) + 5 – 11 ≥ 2(– 3 x) + 2(1) + 5 Simplify. Subtract 7 from both sides. – 11 ≥ – 6 x + 7 – 7 – 18 ≤ – 6 x – 6 Divide both sides by – 6, and reverse the inequality symbol. 3 ≤ x – 9 – 6 – 3 0 3 6 9

Solving Multi-Step Inequalities Check It Out: Example 2 A Solve. Then graph the solution set on a number line. 4 y – 3 – 2 y < 9 2 y – 3 < 9 +3 +3 2 y < 12 2 2 y<6 – 4 – 2 0 2 4 Combine like terms. Add 3 to both sides. Divide both sides by 2. º 6

Solving Multi-Step Inequalities Check It Out: Example 2 B Solve. Then graph the solution set on a number line. – 7 ≥ 2(– 4 x + 1) + 7 – 7 ≥ 2(– 4 x) + 2(1) + 7 Simplify. Subtract 9 from both sides. – 7 ≥ – 8 x + 9 – 9 – 16 ≤ – 8 x – 8 Divide both sides by – 8, and reverse the inequality symbol. 2 ≤ x – 6 – 4 – 2 0 2 4 6

Solving Multi-Step Inequalities WB: Pg. 158

Solving Multi-Step Inequalities Homework: Workbook Pg. 161 #1 -12 even Correct 1 -Step Inequality Quiz -Due Friday -Maximum grade will be a 70