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

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Answer 1 · 2016-09-27T09:30:08

Every $x >= 8$ .

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, $x>=8$ .. , ,

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