Question

Rewrite each equation without absolute value for the given conditions.

y=|x−3|+|x+2|−|x−5|, if x>5
y=|x−3|+|x+2|−|x−5|, if x<-2

Answer 1

y = 2x - 6, if x > 5

y = -4x + 16, if x < -2

Explanation:

When x > 5, the expressions inside the absolute value bars are all positive, so the equation can be rewritten as:

y = (x - 3) + (x + 2) - (x - 5)

y = 2x - 6

When x < -2, the expressions inside the absolute value bars are all negative, so the equation can be rewritten as:

y = -(x - 3) - (x + 2) - -(x - 5)

y = -2x + 6 - 2(x - 5)

y = -4x + 16