Chapter 2: Q. 425 (page 196)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$- 5 \leq 3 x - 2 \leq 4$

Short Answer

Expert verified

The solution of the inequality: $- 1 \leq x \leq 2$

Interval notation: $[- 1, 2]$

The graph of the inequality on number line is:

Step by step solution

Step 1. Given Information.

We have:

$- 5 \leq 3 x - 2 \leq 4$

Step 2. Solve the inequality.

The inequality $- 5 \leq 3 x - 2 \leq 4$ can be written as $- 5 \leq 3 x - 2$ and $3 x - 2 \leq 4$

by using the property of inequality.

First, solve $- 5 \leq 3 x - 2 :$

Switch sides:

$3 x - 2 \geq - 5 3 x - 2 + 2 \geq - 5 + 2 3 x \geq - 3 \frac{3 x}{3} \geq \frac{- 3}{3} x \geq - 1$

Now, solve $3 x - 2 \leq 4$ :

Add $2$ to both sides:

$3 x - 2 + 2 \leq 4 + 2 3 x \leq 6 \frac{3 x}{3} \leq \frac{6}{3} x \leq 2$

Step 3. Draw the solution on the number line.

We have the solution $x \geq - 1$ and $x \leq 2$ .

By combining the both solutions, we get $- 1 \leq x \leq 2$ .

Draw the solution on the number line:

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Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$- 5 \leq 3 x - 2 \leq 4$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the inequality.

Step 3. Draw the solution on the number line.

One App. One Place for Learning.

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Solve the inequality, graph the solution on the number line, and write the solution in interval notation: -5≤3x-2≤4

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the inequality.

Step 3. Draw the solution on the number line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Decision Maths

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$- 5 \leq 3 x - 2 \leq 4$