Chapter 1: Q65. (page 46)

Solve each equation. Check your solutions.
$5 |x - 3| = 65$

Short Answer

Expert verified

The solution set of given equation is $\{16, - 10\}$ .

Step by step solution

– Description of step.

Divide each side of the given equation by 5 and simplify.

\begin{array}{l} \frac{5 |x - 3|}{5} = \frac{65}{5} \\ |x - 3| = 13 \end{array}

– Description of step.

For any real numbers $p$ and $q$ , where $q \geq 0$ ,

Case 1) if $|p| = q$ then $p = q$ or

Case 2) if $|p| = q$ then $p = - q$

– Description of step.

Apply case 1 mentioned in step 2 to $|x - 3| = 13$ and simplify.

\begin{array}{l} x - 3 = 13 \\ x - 3 + 3 = 13 + 3 \\ x = 16 \end{array}

– Description of step.

Apply case 2 mentioned in step 2 to $|x - 3| = 13$ and simplify.

$\begin{array}{l} x - 3 = - 13 \\ x - 3 + 3 = - 13 + 3 \\ x = - 10 \end{array}$

– Description of step.

To check whether the obtained value of $x$ is the solution of given equation, substitute 16 for $x$ into $|x - 3| = 13$ and simplify.

$\begin{array}{l} |x - 3| = 13 \\ |16 - 3| \overset{?}{=} 13 \\ |13| \overset{?}{=} 13 \\ 13 = 13 \end{array}$

– Description of step.

To check whether the obtained value of $x$ is the solution of given equation, substitute $- 10$ for $x$ into $|x - 3| = 13$ and simplify.

\begin{array}{l} |x - 3| = 13 \\ |- 10 - 3| \overset{?}{=} 13 \\ |- 13| \overset{?}{=} 13 \\ 13 = 13 \end{array}

Therefore, the solution set of given equation is $\{16, - 10\}$ .

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 your solutions.
$5 |x - 3| = 65$

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Logic and Functions

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solutions.5x-3=65

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Logic and Functions

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solutions.
$5 |x - 3| = 65$