Question

How do you solve `|2x-5|-2=3`?

Answer 1

`x=0, 5`

Explanation:

First, isolate the absolute value expression by adding 2 to both sides.

`abs(2x-5)-2=3 ->`

`abs(2x-5)-2+2=3+2`

`abs(2x-5)=5`

Now that you got it isolated, you are solving 2 equations. This is due to the absolute of a number and its opposite are the same. If we drop the absolute value, the function becomes:

`2x-5=±5`

Let's solve for x with respect to 5.

`2x-5=5 ->`

`2x-5+5=5+5 ->`

`2x=10 ->`

`(2x)/2=10/2 ->`

`x=5`

Next, solve for x with respect to -5.

`2x-5=-5 ->`

`2x-5+5=-5+5 ->`

`2x=0 ->`

`(2x)/2=0/2 ->`

`x=0`

If you have time you can double check your results by plugging them back in the equation.