Been trying to get through this one for a good couple of hours - I've tried breaking it down into different cases where the expressions are either positive or negative, but that just ends up with "any X", which is wrong.
Maybe you could show your efforts, so we could see where it's going sideways...?
Looking at the three absolute-value break-points: x = -3/2, x = 4, and x = -7. What intervals do these break the number-line into? What do you get when you take the absolute-value bars off, with appropriate signs, on each of these intervals?
For instance, on the interval (-infinty, -7), x + 7 < 0, 2x + 3 < 0, and -x + 4 > 0, so the equation becomes:
. . . . .-(2x + 3) + (-x + 4) = -(x + 7)
. . . . .-2x - 3 - x + 4 = -x - 7
. . . . .-3x + 1 = -x - 7
. . . . .1 + 7 = -x + 3x
. . . . .8 = 2x
. . . . .4 = x
But "x = 4" is not within the interval (-infinity, -7), so this interval has "no solution" (and certainly not "all solution"!).
I can't imagine how you're ending up with "x = x" or some other "true for all values of x" type of solution for each of the intervals. Please do show what you've done, at least for one of the intervals. Thank you!
