Question

|(x/2) + 4| = 1 - x

Solution 1:
x + 8 = 2 - 2x
3x = -6
x = -2

Solution 2:
x + 8 = -2 + 2x
-x = -10
x = 10

Can anybody please explain why the second solution (x=10) doesn't work for this absolute value?

Answer 1

well
1-10=-9, which is negative
however, the absolute value of anything is always positive. Thus, 10 does not satisfy the absolute value equation

Answer 2

Right, so you're saying that from now I should sub the x value into the equation just to make sure that it is a proper solution?

I can see why it doesn't work, but if the solution is not real then why I do I get that answer?

Answer 3

because it's an extraneous solution
the solution arises when you remove the absolute value

Answer 4

sign. The absolute value equation and the one you derived by removing the absolute value sign are not equivalent equations