Chapter 2: Q. 399 (page 195)

Solve each inequality, graph the solution, and write the solution in interval notation.
$- 1 < 3 x + 2 < 8$

Short Answer

Expert verified

Solution of inequality:

$- 1 < x < 2$

Graph the numbers that make both inequalities true:

The solution in interval notation:

$(- 1, 2)$

Step by step solution

Step 1. Given information

Consider the inequality

$- 1 < 3 x + 2 < 8$

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

Subtract 2 to all parts:

$- 1 - 2 < 3 x + 2 - 2 < 8 - 2$

Simplify:

$- 3 < 3 x < 6$

Divide each part by 3:

$\frac{- 3}{3} < \frac{3 x}{3} < \frac{6}{3}$

Simplify:

$- 1 < x < 2$

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

The solution in interval notation:

$(- 1, 2)$

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Solve each inequality, graph the solution, and write the solution in interval notation.
$- 1 < 3 x + 2 < 8$

Short Answer

Step by step solution

Step 1. Given information

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

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

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Solve each inequality, graph the solution, and write the solution in interval notation. −1<3x+2<8

Short Answer

Step by step solution

Step 1. Given information

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve each inequality, graph the solution, and write the solution in interval notation.
$- 1 < 3 x + 2 < 8$