Chapter 1: Q34. (page 44)

Solve each inequality. Graph the solution set on a number line.
$|2 m| \geq 8$

Short Answer

Expert verified

Solution of inequality is $m \leq - 4 or m \geq 4$

Solution set in number line is

Step by step solution

- Definition of absolute value inequality

For real numbers $a and b$ with $b > 0$

Absolute value inequality is $|a| < b$ when $- b < a and a < b$ , and

Absolute value inequality is $|a| > b$ when $a < - b or a > b$

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify 2m≥8

From definition of absolute value inequality, given expression is simplified to

$2 m \leq - 8 or 2 m \geq 8$

Use division property of inequality, divide with same positive number does not reverse the sign of inequality as shown below

$\begin{matrix} \frac{2 m}{2} \leq - \frac{8}{2} or \frac{2 m}{2} \geq \frac{8}{2} \\ m \leq - 4 or m \geq 4 \end{matrix}$

- Graph the solution set

For $m \leq - 4 or m \geq 4$ , number line starts from $- 4$ to $- \infty$ and from 4 to $\infty$

Dot on $- 4 and 4$ shows these points are included in the solution.

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Solve each inequality. Graph the solution set on a number line.
$|2 m| \geq 8$

Short Answer

Step by step solution

- Definition of absolute value inequality

- Write properties of inequality

- Simplify 2m≥8

- Graph the solution set

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Solve each inequality. Graph the solution set on a number line.2m≥8

Short Answer

Step by step solution

- Definition of absolute value inequality

- Write properties of inequality

- Simplify 2m≥8

- Graph the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Probability and Statistics

Geometry

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set on a number line.
$|2 m| \geq 8$