3.4 Solving Multi-Step Inequalities

3.4 Solving Multi-Step Inequalities I can solve multi-step inequalities using inverse operations.

How to Solve • Much like solving a multi-step equation. • Use inverse operations and properties of inequality. • In reverse order.

Practice • 9 + 4t > 21 • 9 + 4t -9 > 21 – 9 • 4t > 12 • t > 3 • Now you try: -6a – 7 ≤ 17

Writing and Solving • We need to use perimeter: p = 2l + 2w • l ≤ 9 ft

Using the Distributive Property • Distribute first, then solve. • 3(t + 1) – 4t ≥ -5 • t ≤ 8 • 15 ≤ 5 – 2(4m + 7) • -3 ≥ m

Variables on Both Sides • 6n – 1 > 3n + 8 • n > 3 • -3b + 12 > 27 – 2b • b < -15

Special Solutions • If variables cancel and you are left with an inequality that is always true, the solution is all real numbers. • Ex: 10 – 8a ≥ 2(5 – 4a) • Distribute: 10 – 8a ≥ 10 – 8a • Add 8a: 10 ≥ 10 • This is ALWAYS true. • Solution: All Real Numbers

Special Solutions • If variables cancel and you are left with an inequality that is never true, there is no solution. • Ex: 6m – 5 > 7m + 7 - m • Combine like terms: 6m – 5 > 6m +7 • Subtract 6m: -5 > 7 • This is NEVER true. • Solution: No Solution

Assignment • ODDS ONLY • P. 190 #9-27, 35-45

3.4 Solving Multi-Step Inequalities