Rewrite the expression without using the absolute-value symbol. |x + 5| , if x ≥ −5 , if x < −5

Answer 1

If x< -5 then x+5 < 0

but the absolute value of x+5 > 0

The absolute value of x+5 then becomes = -(x+5) = -5-x an expression that doesn't need the absolute value symbol

If x is greater than or equal to -5, then x+5 is always greater than or equal to zero and the absolute value symbol is redundant and not needed. The absolute value of x+5 = x+5, when x>-5