The absolute value of any number is the "distance from zero". If the expression is negative, it is converted to positive. The absolute value of x+7 can be either x+7 (if x+7 is positive) or -(x+7) (if x+7 is negative).
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x= -1
|x + 1| - |x + 4| = 0 ∴ |x + 1| = |x + 4| ∴ x + 1 = -x - 4 ∴ 2x = -5 ∴ x = -5/2
x = 7
x=4
Abs(x) = x when x >= 0Abs(x) = -x when x < 0.In short, abs(x) is the distance from the origin to x, irrespective of whether it is to the left or right.