Question

Rewrite without absolute value for the given conditions:
y=|x-3|+|x+2|-|x-5|, if x>5

Answer 1

y = x + 4

Explanation:

Since x > 5, x-3 > 0, x + 2 > 0 and x - 5 > 0

So Ix - 3I = x - 3, Ix + 2I = x + 2 and x - 5 = x - 5

Therefore, y = x - 3 + x + 2 - x + 5

y = x + 4

Answer 2

Explanation:

It might interest you to know what this question means without the restriction. See graph 36b. This shows exactly what happens to the absolute value. There are all sorts of turns and twists in it. Notice all the changes in direction and the minimum at -2,-2. The y intercept is at 0,0.

0,0 is also one of the x intercepts as well. The other is -4,0. The whole point of showing you this is to make you aware of what the restriction does.

The graph is reduced to a line starting at (5,9)