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**Solving Multi-Step Inequalities**

Algebra 1 ~ Chapter 6-3 Solving Multi-Step Inequalities

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**Inequalities that contain more than one operation require more than one step to solve.**

Use inverse operations to undo the operations in the inequality one at a time. ALWAYS check your solution!

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**Example 1 - Solve the inequality and graph the solutions.**

Check, b = 10 45 + 2b > 61 45 + 2(10) > 61 > 61 65 > 61 45 + 2b > 61 – –45 2b > 16 b > 8 Check, b = 6 45 + 2b > 61 45 + 2(6) > 61 > 61 57 > 61 2 4 6 8 10 12 14 16 18 20

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**Ex. 2 - Solve the inequality and graph the solutions.**

– –8 Check, y = -8 8 – 3y ≥ 29 8 – 3(-8) ≥ 29 ≥ 29 32 ≥ 29 –3y ≥ 21 by a negative # y ≤ –7 –10 –8 –6 –4 –2 2 4 6 8 10 –7

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**Check, x = -7 -12 ≥ 3x + 6 -12 ≥ 3(-7) + 6 -12 ≥ -21 + 6 -12 ≥ -15**

Ex. 3 - Solve the inequality and graph the solutions. Check your answer. –12 ≥ 3x + 6 Check, x = -7 -12 ≥ 3x + 6 -12 ≥ 3(-7) + 6 -12 ≥ -12 ≥ -15 –12 ≥ 3x + 6 – – 6 –18 ≥ 3x –6 ≥ x or x ≤ -6 –10 –8 –6 –4 –2 2 4 6 8 10

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**Ex. 4 - Solve the inequality and graph the solutions. Check your answer.**

Check, x = -13 –5 –5 x + 5 < –6 > 3 x < –11 > 3 –20 –12 –8 –4 –16 –11 4 > 3

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**Example 5 - Solve the inequality and graph the solutions.**

Check, x = 2 –4(2 – x) ≤ 8 -4(2 – 2) ≤ 8 -4(0) ≤ 8 0 ≤ 8 −4(2 – x) ≤ 8 –8 + 4x ≤ 8 x ≤ 4 –10 –8 –6 –4 –2 2 4 6 8 10

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**Example 6 - Solve the inequality and graph the solutions**

Example 6 - Solve the inequality and graph the solutions. Check your answer. 3 + 2(x + 4) > 3 3 + 2(x + 4) > 3 Check, x = 0 3 + 2(x + 4) > 3 3 + 2(0 + 4) > 3 3 + 2(4) > 3 3 + 8 > 3 11 > 3 3 + 2x + 8 > 3 2x + 11 > 3 – 11 – 11 2x > –8 x > –4 –10 –8 –6 –4 –2 2 4 6 8 10

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**Lesson Review Solve each inequality and graph the solutions. x ≤ –4**

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**Assignment Worksheet 6-3 Pages 335-336 #’s 16-28 (evens),**

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