Chapter 1: Q59. (page 39)

Solve each equation. Check the solution.
59. If $|x - 3| = 17$

Short Answer

Expert verified

The value of $x$ is $20$ and $- 14$ .

Step by step solution

- State the definition of absolute value.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

- Solve the inequality.

If $x$ is a number, then absolute value of $x$ is written as $|x|$ .

Here, the inequality is:

$|x - 3| = 17$

Case 1:

$\begin{matrix} a = b \\ x - 3 = 17 \\ x - 3 + 3 = 17 + 3 \\ x = 20 \end{matrix}$

Or Case 2:

$\begin{matrix} a = - b \\ x - 3 = - 17 \\ x - 3 + 3 = - 17 + 3 \\ x = - 14 \end{matrix}$

The solution is $20$ and $- 14$

- Check the solution.

For case 1: $x = 20$ .

Check:

$\begin{array}{r} |x - 3| = 17 \\ |20 - 3| = 17 \\ |17| = 17 \\ 17 = 17 \end{array}$

Thus, it is correct.

For case 2: $x = - 14$ .

Check:

$\begin{array}{r} |x - 3| = 17 \\ |- 14 - 3| = 17 \\ |- 17| = 17 \\ 17 = 17 \end{array}$

Thus, it is also correct.

- State the conclusion.

Therefore, the solution set for $x$ is $\{20, - 14\}$ .

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 equation. Check the solution.
59. If $|x - 3| = 17$

Short Answer

Step by step solution

- State the definition of absolute value.

- Solve the inequality.

- Check the solution.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Logic and Functions

Decision Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Solve each equation. Check the solution.59. If x-3=17

Short Answer

Step by step solution

- State the definition of absolute value.

- Solve the inequality.

- Check the solution.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Logic and Functions

Decision Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Solve each equation. Check the solution.
59. If $|x - 3| = 17$