Question

How do you solve `abs(4x - 2) = 10`?

Answer 1

`x = 3` or `x=-2`.

Explanation:

You're dealing with an absolute value equation, which means that you need to take into account two possibilities for the modulus

• if `4x-2>=0`, you have

`|4x-2| = 4x-2`

and the equation becomes

`4x-2 = 10`

`4x = 12 implies x = 12/4 = color(green)(3)`

• If `4x-2<0`, then you have

`|4x-2| = -(4x-2) = -4x+2`

and the equation becomes

`-4x+2 = 10`

`-4x = 8 implies x = 8/(-4) = color(green)(-2)`

So, your equation has two possible solutions: `x=3` or `x=-2`.