Find the product of all real values of that satisfy the equation .

Source: NCTM Mathematics Teacher, January 2006

**SOLUTION**

One way to interpret the absolute values and is to think of them as the distances from point to point and from point to point on the number line

We want to find the points such that .

Case 1: is between and

If we divide segment into equal parts by drawing a series of parallel lines and place as shown in the above figure, then clearly .

Case 2: is not between and

If we divide segment into equal parts and place by the same equal part from B, then .

Product of all values

**Answer**:

**Alternative solution 1**

**
**If we plot the two functions and , the graphs intersect at two points and .

Multiplying the two values yields

**Alternative solution 2**

If and .

If and .