Question

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

Answer 1

`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`

Answer 2

`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"`