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Chapter 2: Q. 397 (page 195)

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

鈭�3<2x鈭�5鈮�1

Short Answer

Expert verified

Solution of inequality:

1<x鈮�3

Graph the numbers that make both inequalities true:

The solution in interval notation:

(1,3]

Step by step solution

01

Step 1. Given information 

Consider the inequality

鈭�3<2x鈭�5鈮�1

02

Step 2. Solve the inequality−3 < 2x − 5 ≤ 1

Add 5 to all parts:

鈭�3+5<2x鈭�5+5鈮�1+5

Simplify:

2<2x鈮�6

Divide each part by 2:

22<2x2鈮�62

Simplify:

1<x鈮�3

03

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

The solution in interval notation:

(1,3]

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