|(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?

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

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?

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

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

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