Question

How do you solve `1/2abs(4x – 8) - 7 = 3`?

Answer 1

Rearrange and split into cases to find: `x = 7` or `x = -3`

Explanation:

First add `7` to both sides to get:

`1/2abs(4x-8)=10`

Divide both sides by `2` to get:

`5 = 1/4abs(4x-8) = abs(x-2)`

There are now two cases:

Case 1 : (x - 2) >= 0

If `(x - 2) >= 0` then `abs(x-2) = (x-2)` and we have:

`5 = x-2`, hence `x = 7`

This is a valid solution since `x - 2 = 7 - 2 > 0` thus satisfying the condition of the case.

Case 2 : (x - 2) < 0

If `(x - 2) < 0` then `abs(x-2) = -(x-2) = 2 - x` and we have:

`5 = 2-x`, hence `x = -3`

This is a valid solution since `x - 2 = -3 -2 < 0` thus satisfying the condition of the case.