Question

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

Answer 1

`x=1/3" or " x=5`

Explanation:

There are 2 possible solutions to the equation.

`2x-3=color(red)(+-)(x+2)`

`color(blue)"first solution"`

`2x-3=x+2`

`"subtract x from both sides."`

`2x-x-3=cancel(x)cancel(-x)+2`

`rArrx-3=2`

`"add 3 to both sides."`

`xcancel(-3)cancel(+3)=2+3`

`rArrx=5`

`color(blue)"second solution"`

`2x-3=-x-2`

`rArr3x=1`

`rArr x=1/3`

`color(blue)"As a check"`

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

`"left side "=|(2xx5)-3|=|7|=7`

`"right side "=|5+2|=|7|=7`

`"left side "=|2/3-3|=|-2 1/3|=2 1/3`

`"right side "=|1/3+2|=|2 1/3|=2 1/3`

`rArrx=1/3" or " x=5" are the solutions"`