How do you solve abs(2x-3)=5?

2 Answers
Jun 19, 2018

x=-1

x=4

Explanation:

As explained below:

Step 1: Clear the absolute value bars

|2x-3|=5

For negative part, lets use -(2x-3)

For positive part, lets use (2x-3)

Step 2: Solve the negative part

-(2x-3) = 5

-2x+3 = 5

-2x=5-3

-2x=2

x=-2/2 = -1

x=-1 ----> solution for the negative part

Step 3: Solve the positive part

(2x-3)=5

2x=5+3

2x=8

x=8/2

x=4 ------> solution for the positive part

So values of x are x=-1 and x=4

Jun 19, 2018

x=-1" or "x=4

Explanation:

"the expression inside the absolute value can be positive"
"or negative"

color(magenta)"positive expression"

2x-3=5rArr2x=5+3=8rArrx=4

color(magenta)"negative expression"

-(2x-3)=5

-2x+3=5

-2x=5-3=2

x=2/(-2)=-1

color(blue)"As a check"

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

x=-1

|-2-3|=|-5|=5

x=4

|8-3|=|5|=5

x=-1" or "x=4" are the solutions"