Chapter 1: Q11. (page 44)

Solve each inequality. Graph the solution set on a number line.
$|g + 4| \leq 9$ .

Short Answer

Expert verified

The solution of the given inequality is $- 13 \leq g \leq 5$ .

Step by step solution

-Write the inequalities

A For all real numbers a, b and $b > 0$ ; it is true that if $|a| \leq b$ then $- b < a < b$ . The given absolute inequality is $|g + 4| \leq 9$ .

– Apply the definition of an absolute compound inequality

Use the definition of absolute value inequality and write the compound inequality as follows:

$\begin{matrix} | g + 4 | \leq 9 \\ - 9 \leq g + 4 \leq 9 \\ - 9 - 4 \leq g + 4 - 4 \leq 9 - 4 \\ - 13 \leq g \leq 5 \end{matrix}$

Therefore, the solution of the given absolute inequality is $- 13 \leq g \leq 5$

– Graph of the solution set

The graph for the inequality $- 13 \leq g \leq 5$ is as shown below

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Solve each inequality. Graph the solution set on a number line.
$|g + 4| \leq 9$ .

Short Answer

Step by step solution

-Write the inequalities

– Apply the definition of an absolute compound inequality

– Graph of the solution set

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Solve each inequality. Graph the solution set on a number line.g+4≤9.

Short Answer

Step by step solution

-Write the inequalities

– Apply the definition of an absolute compound inequality

– Graph of the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Geometry

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set on a number line.
$|g + 4| \leq 9$ .