If w and are numbers, which of the following expressions will always be the distance between w and Q

on the number line?

Choose 1 answer:

A. |w - q|

B. |w + q|

C. w - q

D. q - w

Answer: Choice A. |w - q|

Let's say for example that w = 10 and q = 7. This means the distance between these values is w-q = 10-7 = 3. This is the distance between w and q.

Now let's make q larger. If w = 12 and q = 20, then w-q = 12-20 = - 8 assuming we subtract in the same order. We use absolute value bars to ensure the result is positive. So instead we say

|w - q| = |12 - 20| = | - 8 | = 8

Distance is never negative.