Question

Write each of the following expressions without using absolute value:
|y-x| if y>x

Answer 1

y - x

Explanation:

You want the simplified form of |y -x| if y > x.

Absolute value

The absolute value function is defined as ...

|a| = a . . . . for a ≥ 0

|a| = -a . . . . for a < 0

Application

We have the expression |y -x|. Using the above function rule, it is ...

|y -x| = y -x . . . . for y -x ≥ 0 ⇒ y ≥ x

|y -x| = -(y -x) = x -y . . . . for y -x < 0 ⇒ y < x

The problem statement tells us we're interested in the case y > x, so the first version applies:

|y -x| = y -x . . . . if y > x