Greater Than: Outside

The inequality |x| > 3 asks for the numbers more than three steps from zero, in either direction. Those are the numbers above 3 and the numbers below -3. The answer has two separate pieces, joined by "or":

x > 3

or

x < -3

|x| > 3: more than three steps from zero, on either side

When an absolute value is greater than a number, it splits into two cases: |u| > c becomes u > c or u < -c. Look at the second case. A number far below zero is less than -c, so the sign turns around with the minus. "Less than" gives a chain, the numbers between. "Greater than" gives an "or", the numbers outside. Draw each one on a number line to remember which is which.