Question

Why does the solution for an absolute value equation or inequality typically result in a pair of equations or inequalities?

Answer 1

And represents the distance between a and 0 on a number line. Has two solutions x = a and x = -a because both numbers are at the distance a from 0. This holds true for all absolute value inequalities. ... Because by definition, the absolute value of a number is its distance from 0 on a number line which means that there are two such numbers: a positive/negative number