1. 4.4 Solving Multi-step Inequalities

2. 4.4 – Solving Multi-step Inequal. Goals / “I can…”  Solve multi-step inequalities with variables on one side  Solve multi-step inequalities with variables on both sides

3. 4.4 – Solving Multi-step Inequal. Up to this point, we have shown that inequalities (, ≤, ≥) are solved just like equalities (=), unless the coefficient is negative, then you switch the inequality. Therefore, we can solve multi-step inequalities just like multi-step equalities.

4. 4.4 – Solving Multi-step Inequal. Example: 2x + 5 < 15 -5 -5 subtract 5 2x < 10 2 2divide by 2 x < 5

5. 4.4 – Solving Multi-step Inequal. Example 2 -3x – 7 >14 +7 +7add 7 -3x > 21 -3 -3divide by -3 x < -7 SWITCH SYMBOL!!!!!! (you divided by a negative)

6. 1) Solve 5m - 8 > 12 + 8 + 8 5m > 20 5 5 m > 4 5(4) – 8 = 12 1.Draw “the river” 2.Add 8 to both sides 3.Simplify 4.Divide both sides by 5 5.Simplify 6.Check your answer 7.Graph the solution o 453

7. 2) Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-2) = 18 1.Draw “the river” 2.Subtract 12 from both sides 3.Simplify 4.Divide both sides by -3 5.Simplify (Switch the inequality!) 6.Check your answer 7.Graph the solution o -2-3

8. Which graph shows the solution to 2x - 10 ≥ 4? 1.. 2. 3. 4. Answer Now

9. 3) Solve 5m - 4 < 2m + 11 -2m 3m - 4 < 11 + 4 + 4 3m < 15 3 3 m < 5 5(5) – 4 = 2(5) + 11 1.Draw “the river” 2.Subtract 2m from both sides 3.Simplify 4.Add 4 to both sides 5.Simplify 6.Divide both sides by 3 7.Simplify 8.Check your answer 9.Graph the solution o 564

10. 2r - 18 ≤ 5r + 3 4) Solve 2r - 18 ≤ 5r + 3 -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3 -7 ≤ r or r ≥ -7 2(-7) – 18 = 5(-7) + 3 1.Draw “the river” 2.Subtract 2r from both sides 3.Simplify 4.Subtract 3 from both sides 5.Simplify 6.Divide both sides by 3 7.Simplify 8.Check your answer 9.Graph the solution ● -7-6-8

11. 6) Solve -2x + 6 ≥ 3x - 4 1.x ≥ -2 2.x ≤ -2 3.x ≥ 2 4.x ≤ 2 Answer Now

12. 5) Solve 26p - 20 > 14p + 64 -14p 12p – 20 > 64 + 20 + 20 12p > 84 12 12 p > 7 26(7) – 20 = 14(7) + 64 1.Draw “the river” 2.Subtract 14p from both sides 3.Simplify 4.Add 20 to both sides 5.Simplify 6.Divide both sides by 12 7.Simplify 8.Check your answer 9.Graph the solution o 786

13. What are the values of x if 3(x + 4) - 5(x - 1) < 5? Answer Now 1.x < -6 2.x > -6 3.x < 6 4.x > 6

14. 4.4 – Solving Multi-step Inequal. Example 3 7 + 6a > 19

15. 4.4 – Solving Multi-step Inequal. Example 3 2(r + 2) – 3r ≥ -1

16. 4.4 – Solving Multi-step Inequal. Example 4 6z - 15 < 4z + 11