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Chapter 1: Q36. (page 49)

Solve the equation and check the solution.

|4x-5|=-25

Short Answer

Expert verified

No solution.

Step by step solution

01

Step 1- Apply the concept of absolute value.

For any real numbers a,b, where b鈮�0, if |a|=b then a=b or a=-b.

02

Step 2- Step description.

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

Use the concept of absolute value equation as follows:

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

03

Step 3- Step description.

Case 1. Simplify 4x-5=25.

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

4x鈭�5=254x鈭�5鈭�25=25鈭�254x鈭�30=04x=30x=304

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

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

4x鈭�5=鈭�254x鈭�5+25=鈭�25+254x+20=04x=鈭�20x=鈭�204x=鈭�5

As the solution is negative, but the absolute value cannot be negative, therefore no solution for x鈭�鈩�.

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