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Chapter 2: Q. 415 (page 196)

Solve each inequality, graph the solution, and write the solution in interval notation.

34x+2鈮�鈭�1or12(x+8)鈮�鈭�3

Short Answer

Expert verified

Solution of inequalities

x鈮�-4orx鈮�-14

Graph of solution of inequalities

The solution in interval notation

(-鈭�,鈭�)

Step by step solution

01

Step 1. Given information 

Consider each inequality

34x+2鈮�鈭�1or12(x+8)鈮�鈭�3

02

Step 2. Solve each inequality 

34x+2鈮�鈭�134x鈮�-1-234x鈮�-3x鈮�-3脳43x鈮�-4 or 12(x+8)鈮�鈭�3x+8鈮�-3脳2x+8鈮�-6x鈮�-6-8x鈮�-14

03

Step 3. Graph each inequality  

Forx鈮�-4

Forx鈮�-14

04

Step 4. Graph number that make either one inequality true x≤-4 or x≥-14

The solution in interval notation

(-鈭�,-4]鈭�[-14,鈭�)=(-鈭�,鈭�)

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