Chapter 1: Q36. (page 49)

Solve the equation and check the solution.
$| 4 x - 5 | = - 25$

Short Answer

Expert verified

No solution.

Step by step solution

Step 1- Apply the concept of absolute value.

For any real numbers $a, b$ , where $b \geq 0$ , if $| a | = b$ then $a = b$ or $a = - b$ .

Step 2- Step description.

Consider the equation $| 4 x - 5 | = - 25$ .

Use the concept of absolute value equation as follows:

$4 x - 5 = - 25$ or $4 x - 5 = 25$ .

Step 3- Step description.

Case 1. Simplify $4 x - 5 = 25$ .

Subtract 25 from both sides of the equation and simplify as follows:

$\begin{array}{l} 4 x - 5 = 25 \\ 4 x - 5 - 25 = 25 - 25 \\ 4 x - 30 = 0 \\ 4 x = 30 \\ x = \frac{30}{4} \end{array}$

Case 2. Simplify $4 x - 5 = - 25$ .

Add 25 on both sides of the equation and simplify as follows:

$\begin{array}{l} 4 x - 5 = - 25 \\ 4 x - 5 + 25 = - 25 + 25 \\ 4 x + 20 = 0 \\ 4 x = - 20 \\ x = \frac{- 20}{4} \\ x = - 5 \end{array}$

As the solution is negative, but the absolute value cannot be negative, therefore no solution for $x \in ℝ$ .

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 the equation and check the solution.
$| 4 x - 5 | = - 25$

Short Answer

Step by step solution

Step 1- Apply the concept of absolute value.

Step 2- Step description.

Step 3- Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Decision Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the equation and check the solution.|4x-5|=-25

Short Answer

Step by step solution

Step 1- Apply the concept of absolute value.

Step 2- Step description.

Step 3- Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Decision Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the equation and check the solution.
$| 4 x - 5 | = - 25$