Chapter 5: Q35. (page 324)

Solve each inequality. Then graph the solution set.
$| x - 4 | < 9$

Short Answer

Expert verified

The solution for the given inequality $|x - 4| < 9$ is localid="1647431389629" $x \in (- 5, 13)$ .

The graph of the solution set which is $x \in (- 5, 13)$ is:

Step by step solution

Step 1. Solve the given inequality |x−4|<9.

The solution of the given inequality $|x - 4| < 9$ is:

Case 1: $x - 4$ is non-negative.

$\begin{matrix} x - 4 < 9 \\ x - 4 + 4 < 9 + 4 \\ x < 13 \\ x \in (- \infty, 13) \end{matrix}$

Case 2: $x - 4$ is negative.

$\begin{matrix} - (x - 4) < 9 \\ (- 1) (- (x - 4)) > (- 1) (9) \\ x - 4 > - 9 \\ x - 4 + 4 > - 9 + 4 \\ x > - 5 \\ x \in (- 5, \infty) \end{matrix}$

The solution of the inequality $|x| \leq a$ is $x \geq - a$ and $x \leq a$ .

That implies the solution of the inequality $|x| \leq a$ is the intersection of the solutions of the inequalities $x \geq - a$ and $x \leq a$ .

Find the intersection of the solutions of the inequalities $x - 4 < 9$ and $x - 4 > - 9$ to find the solution of the inequality $|x - 4| < 9$ .

The intersection of the solutions of the inequalities $x - 4 < 9$ and $x - 4 > - 9$ is: $x \in (- 5, 13)$

Therefore, the solution of the inequality $|x - 4| < 9$ is $x \in (- 5, 13)$ .

Step 2. Draw the graph of the solution set which is x∈(−5,13).

The graph of the solution set which is $x \in (- 5, 13)$ is:

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Solve each inequality. Then graph the solution set.
$| x - 4 | < 9$

Short Answer

Step by step solution

Step 1. Solve the given inequality |x−4|<9.

Step 2. Draw the graph of the solution set which is x∈(−5,13).

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Solve each inequality. Then graph the solution set.|x−4|<9

Short Answer

Step by step solution

Step 1. Solve the given inequality |x−4|<9.

Step 2. Draw the graph of the solution set which is x∈(−5,13).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Then graph the solution set.
$| x - 4 | < 9$