3.4 Solving Two-Step and Multi-Step Inequalities

1. 3.4 Solving Two-Step and Multi-Step Inequalities Algebra 4.0, 5.0 Solve inequalities that contain more than one operation.

2. Main Idea • When we solve multi-step equations: • We use more than one operation • We use inverse operations • We may need to combine like terms • We may need to use the distributive property • We may need to multiply reciprocals to get rid of fractions • All these items hold true for inequalities • What do we need to be careful of?

3. -12 > 3x + 6 8 – 3y > 29 Two-Step Inequalities: Practice

4. Example-Solving Multi-Step Inequalities • Solve and graph solution

5. –8 + 4x ≤ 8 +8 +8 –8 –10 –6 –4 0 2 4 6 8 –2 10 Example: Distributive Property Solve the inequality and graph the solutions. –4(2 – x) ≤ 8 −4(2 – x) ≤ 8 Distribute –4 on the left side. −4(2) − 4(−x) ≤ 8 Since –8 is added to 4x, add 8 to both sides. 4x ≤16 Since x is multiplied by 4, divide both sides by 4 to undo the multiplication. x ≤ 4 The solution set is {x:x ≤ 4}.

6. – 11 –11 10 –8 –10 –6 –4 0 2 4 6 8 –2 Example: Distributive Property & Combine Like Terms Solve the inequality and graph the solutions. Check your answer. 3 + 2(x + 4) > 3 Distribute 2 on the left side. 3 + 2(x + 4) > 3 3 + 2x + 8 > 3 Combine like terms. 2x + 11 > 3 Since 11 is added to 2x, subtract 11 from both sides to undo the addition. 2x > –8 Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. x > –4 The solution set is {x:x > –4}.

7. Multi-Step Practice • Solve and graph solution.

8. Example-Simplify before Solving • Solve and graph solutions

9. Example-Simplify before Solving • Solve and graph solutions

10. Example-Simplify before Solving • Solve and graph solutions

11. Practice • Solve and graph solutions

12. Review • What is important to remember when solving inequalities? • What is difficult when solving multi-step inequalities?