I've never seen this problem! Kind of cool. I'm sure there are a lot of approaches, but I would divide the problem by the values of x that require a sign change from the absolute value:
x < -2, -2 ≤ x < 1, 1 ≤ x < 5, x ≥ 5
If the inside of the absolute value is positive, you can remove the absolute value sign. If the inside expression is negative you can multiply by negative 1 (change all the signs) and remove the sign.
x ≥ 5 (easiest, just remove all the signs) (x+2) + (x-5) + (x-1) = 3x - 4
1 ≤ x < 5: (x+2) + (5-x) + x-1 = x+6
-2 ≤ x < 1: (x +2) + (5-x) + (1 - x) =
x < -2 :
I've left some for you to do. You now have 4 equations for four different values of x that work.
I'll do the first one: 3x-4 = 12 3x = 16 x = 16/3 One last thing... we specified x ≥ 5 for this equation, so this is NOT a valid answer.
Looks like the next one isn't either. (Only the fourth equation works...)
Good luck!
