3 4 Solving TwoStep and MultiStep Inequalities Algebra

3. 4 Solving Two-Step and Multi-Step Inequalities ? ? ? Algebra 4. 0, 5. 0 Solve inequalities that contain more than one operation.

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? ? ? ?

Two-Step Inequalities: Practice 1) -12 > 3 x + 6 2) 8 – 3 y > 29 ? ? ?

Example-Solving Multi-Step Inequalities • Solve and graph solution ? ? ?

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

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 + 2 x + 8 > 3 2 x + 11 > 3 – 11 2 x Combine like terms. Since 11 is added to 2 x, subtract 11 from both sides to undo the addition. Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. The solution set is {x: x > – 4}. > – 8 x > – 4 – 10 – 8 – 6 – 4 – 2 ? ? ? 0 2 4 6 8 10