Chapter 2: Q. 420 (page 196)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$- 5 \leq 2 x - 1 < 7$

Short Answer

Expert verified

The solution of the inequality is $- 2 \leq x < 4$

Interval notation: $[- 2, 4)$

The graph of the inequality on number line is:

Step by step solution

Step 1. Given Information.

We have:

$- 5 \leq 2 x - 1 < 7$

Step 2. Solve the compound inequality.

The inequality $- 5 \leq 2 x - 1 < 7$ can be written as $- 5 \leq 2 x - 1$ and $2 x - 1 < 7$ by using the property of inequality.

First, solve $- 5 \leq 2 x - 1$

Switch sides:

$2 x - 1 \geq - 5 2 x - 1 + 1 \geq - 5 + 1 2 x \geq - 4 \frac{2 x}{2} \geq \frac{- 4}{2} x \geq - 2$

Interval notation: $[- 2, \infty)$

Now, solve $2 x - 1 < 7$ :

$2 x - 1 + 1 < 7 + 1 2 x < 8 \frac{2 x}{2} < \frac{8}{2} x < 4$

Interval notation: $(- \infty, 4)$

Step 3. Draw the solution on the number line.

We have the solution $x \leq - 2$ and $x > 4$ .

By combining the both solutions, we get $- 2 \leq x < 4$ .

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:
$- 5 \leq 2 x - 1 < 7$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the compound inequality.

Step 3. 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≤2x-1<7

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the compound 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

Statistics

Mechanics Maths

Probability and Statistics

Logic and Functions

Geometry

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:
$- 5 \leq 2 x - 1 < 7$