Exercise 54 Page 46

Absolute values can be interpreted as the distance away from a midpoint. For one-variable absolute value equations, this distance can be represented by two points on a number line, such as the one given in the exercise.

Because our equation needs a distance from a midpoint, we should begin by finding the halfway point between the two given values. We can do this by calculating their mean. Mean=- 3+ 3/2= 0 Now we need to find the distance between this midpoint and each of the given points.

We see that both -3 and 3 are 3 units away from 0. Written as an equation, we can show that the difference between a number x and the midpoint is equal to the distance we found above. |x- midpoint|=distance |x- 0|=3 Let's simplify the equation. |x-0|=3 ⇒ |x|=3