We are asked to explain why both the positive and the negative equations must be set up when solving absolute value equations.
To answer this question, we need to review what absolute value means. Absolute value refers to the distance of a number from zero regardless of the direction, which is indicated by the signs (positive if to the right of zero, and negative if to its left).
Therefore, when solving absolute value equations, we must provide all possible answers that are of the same distance from zero. That means solving for the positive equation, which gives us the number to the right of zero, as well as solving for the negative equation, which gives us the number to the left of zero with the given distance (absolute value).