3.4 Solving Multi-Step Inequalities

1. 3.4 Solving Multi-Step Inequalities SWBAT solve inequalities with variables on one side. SWBAT solve inequalities with variables on both sides.

2. Do Now Solve each equation. • 3(c + 4) = 6 • 3t + 6 = 3(t – 2) • 5p + 9 = 2p – 1 • 7n + 4 – 5n = 2(n + 2)

3. Solving Inequalities with Variables on One Side • Sometimes you need more than one step to solve an equation, and the same is true with inequalities. • Just as with equations, you undo addition and subtraction first and then multiplication and division.

4. Example 1 • Solve 7 + 6a > 19 and graph. • Check the solution.

5. Example 2 • Solve 2(t + 2) – 3t > -1 and graph. • Check your solution.

6. More Examples • -3x – 4 < 14 • 5 < 7 – 2t • 4p + 2(p + 7) < 8 • 15 < 5 – 2(4m + 7) • The school band needs a banner to carry in a parade. The banner committee decides that the length of the banner should be 18 feet. What are the possible widths of the banner if they can use no more than 48 feet of trim? • To make a second banner, the committee decided to make the length 12 feet. They have 40 feet of a second type of trim. Write and solve an inequality to find the possible widths of the second banner.

7. Solving Inequalities with Variables on Both Sides • Step 1: Find like terms. • Step 2: Combine like terms on each side of the equal sign (if necessary). • Step 3: Move variable terms to one side of the equal sign by addition or subtraction. • Step 4: Isolate the variable by multiplication or division (if necessary).

8. Example 1 • Solve 6z – 15 < 4z + 11

9. Example 2 • Solve -3(4 – m) > 4(2m + 1)

10. Example 3 • Solve -6(x – 4) > 7(2x – 3)

11. Independent Practice • p. 155 # 13 – 27 odd

12. Homework • p. 155 #29 – 29 odd, 52