Chapter 5: Q39. (page 324)

Solve each inequality. Then graph the solution set.
$| 3 d - 1 | \leq 8$

Short Answer

Expert verified

The solution for the given inequality $|3 d - 1| \leq 8$ is $d \in [- \frac{7}{3}, 3]$ .

The graph of the solution set which is is $d \in [- \frac{7}{3}, 3]$ :

Step by step solution

Step 1. Solve the given inequality |3d−1|≤8.

The solution of the given inequality $|3 d - 1| \leq 8$ is:

Case 1: $3 d - 1$ is non-negative.

$\begin{matrix} 3 d - 1 \leq 8 \\ 3 d - 1 + 1 \leq 8 + 1 \\ 3 d \leq 9 \\ \frac{3 d}{3} \leq \frac{9}{3} \\ d \leq 3 \\ d \in (- \infty, 3] \end{matrix}$

Case 2: $3 d - 1$ is negative.

$\begin{matrix} - (3 d - 1) \leq 8 \\ (- 1) (- (3 d - 1)) \geq (- 1) (8) \\ 3 d - 1 \geq - 8 \\ 3 d - 1 + 1 \geq - 8 + 1 \\ 3 d \geq - 7 \\ \frac{3 d}{3} \geq \frac{- 7}{3} \\ d \geq - \frac{7}{3} \\ d \in [- \frac{7}{3}, \infty) \end{matrix}$

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 $3 d - 1 \leq 8$ and $3 d - 1 \geq - 8$ to find the solution of the inequality $|3 d - 1| \leq 8$ .

The intersection of the solutions of the inequalities $3 d - 1 \leq 8$ and $3 d - 1 \geq - 8$ is:

$d \in [- \frac{7}{3}, 3]$

Therefore, the solution of the inequality $|3 d - 1| \leq 8$ is $d \in [- \frac{7}{3}, 3]$ .

Step 2. Draw the graph of the solution set which is d∈[−73,3].

The graph of the solution set which is $d \in [- \frac{7}{3}, 3]$ is:

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each inequality. Then graph the solution set.
$| 3 d - 1 | \leq 8$

Short Answer

Step by step solution

Step 1. Solve the given inequality |3d−1|≤8.

Step 2. Draw the graph of the solution set which is d∈[−73,3].

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Pure Maths

Logic and Functions

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Then graph the solution set.|3d−1|≤8

Short Answer

Step by step solution

Step 1. Solve the given inequality |3d−1|≤8.

Step 2. Draw the graph of the solution set which is d∈[−73,3].

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Pure Maths

Logic and Functions

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Then graph the solution set.
$| 3 d - 1 | \leq 8$