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

1 Answer
Sep 27, 2016

Answer:

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#.. , ,