Absolute Value Inequalities

An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

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

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

It represents the values of x that are within a distance d from c on the number line.

It represents the values of x that are more than a distance d away from c on the number line.

The first step is to separate it into two inequalities: -8x < 8 and -8x > -8.

This means that x can take any value between 0 and 8, not including 0 and 8.

The 'and' indicates that both conditions must be satisfied simultaneously.

The 'or' indicates that at least one of the conditions must be satisfied.

You graph the solution on a number line, shading the appropriate regions based on the solution set.