Question 1155747
if the expression is positive, then the absolute value of the expression will be the expression.
if the expression is negative, then the absoolute value of the expression will be minus the expression.
when x = -1/2, abs(-1/2) = -1 * -1/2 = 1/2
when x = 1/2, abs(1/2) = 1/2
in both cases, abs(x) = 1/2
when you solve for x, you do the following:
if x is positive, then abs(x) = 1/2 becomes x = 1/2
when x is negative, then abs(x) = 1/2 becomes -x = 1/2
solve for x to get x = -1/2
what this says is that, when absw(x) = 1/2, then x = plus or minus 1/2.
in both cases, abs(x) will be equal to 1/2


here's a reference, one of several that can be found on the internet.


<a href = "https://www.purplemath.com/modules/solveabs.htm" target = "-blank">https://www.purplemath.com/modules/solveabs.htm</a>