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Chapter 2: Q. 399 (page 195)

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

鈭�1<3x+2<8

Short Answer

Expert verified

Solution of inequality:

鈭�1<x<2

Graph the numbers that make both inequalities true:

The solution in interval notation:

(-1,2)

Step by step solution

01

Step 1. Given information 

Consider the inequality

鈭�1<3x+2<8

02

Step 2. Solve the inequality  −1 < 3x + 2 < 8

Subtract 2 to all parts:

鈭�1-2<3x+2-2<8-2

Simplify:

鈭�3<3x<6

Divide each part by 3:

鈭�33<3x3<63

Simplify:

鈭�1<x<2

03

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

The solution in interval notation:

(-1,2)

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