Question

How do you solve `|x-8|=|2-x|-6`?

Answer 1

Every `x >= 8`.

Explanation:

Consider the cases #(i) x<=2 (ii) x >=2 and x<= 8 and (iii x >= 8.

Case (i): the equation becomes `8-x=2-x - 6 to 8=-4`. So, cross it.

Likewise,

Case (ii) :`8-x=x-2-6 to x=8`

Case (ii): `x-8=x-2-6 to 8 = 8. So, every`x>=2 is a solution.

And so, altogether, `x>=8`.. , ,