Greater Than: Outside

The inequality $\left|x\right| > 3$ 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: $\left|u\right| > c$ 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.