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Chapter 2: Q. 400 (page 195)

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

鈭�8<5x+2鈮�鈭�3

Short Answer

Expert verified

Solution of inequality:

鈭�2<x鈮�鈭�1

Graph the numbers that make both inequalities true:

The solution in interval notation:

(-2,-1]

Step by step solution

01

Step 1. Given information  

Consider the inequality

鈭�8<5x+2鈮�鈭�3

02

Step 2. Solve the inequality  −8 < 5x + 2 ≤ −3

Subtract 2 to all three parts:

鈭�8-2<5x+2-2鈮�鈭�3-2

Simplify:

鈭�10<5x鈮�鈭�5

Divide each part by 5:

鈭�105<5x5鈮�鈭�55

Simplify:

鈭�2<x鈮�鈭�1

03

Step 3. Graph the solution of inequality  −2 < x ≤ −1

The solution in interval notation:

(-2,-1]

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