The Equation |x| = 3

The equation |x| = 3 asks which numbers are three steps from zero. There are two of them, 3 and -3. An absolute value equation usually has two solutions, one on each side of zero:

x = 3

or

x = -3

The one equation |x| = 3 splits into two ordinary equations, and both answers count. Check each one: |3| = 3 and |-3| = 3.

To solve an absolute value equation, split it into two cases: |u| = c becomes u = c or u = -c. After the split, each case is an ordinary equation. Solve each case the way you already know, and keep both answers.