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Chapter 2: Q. 413 (page 195)

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

2(x+3)鈮�0or3(x+4)鈮�6

Short Answer

Expert verified

Solution of inequalities

x鈮�-3orx鈮�-2

Graph of solution of inequalities

The solution in interval notation

(-鈭�,鈭�)

Step by step solution

01

Step 1. Given information 

Consider the inequality

2(x+3)鈮�0or3(x+4)鈮�6

02

Step 2. Solve each inequality 

2(x+3)鈮�0x+3鈮�02x+3鈮�0x鈮�0-3x鈮�-3or3(x+4)鈮�6x+4鈮�63x+4鈮�2x鈮�2-4x鈮�-2

03

Step 3. Graph each inequality 

Forx鈮�-3

Forx鈮�-2

04

Step 4. Graph number that make either one inequality true x≥-3 or x≤-2

The solution in interval notation

(-鈭�,-2]鈭�[-3,鈭�)=(-鈭�,鈭�)

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