Absolute Value Inequalities

An absolute value inequality is an inequality that involves the absolute value of a variable expression, indicating the distance of the expression from zero on a number line.

To solve |x| < a, you split it into two inequalities: -a < x < a.

To solve |x| > a, you split it into two inequalities: x < -a or x > a.

The solution represents the values of p that are either less than or equal to -13 or greater than or equal to 7.

The solution is -12 ≤ x ≤ 4.

This means that x is between -14 and 1, not including the endpoints.

The solution is -6 < x < 1.

It implies that x is between -4/3 and 6.

The graph shows an open interval on the number line between -a and a.

The graph shows two open intervals: (-∞, -a) and (a, ∞).