Solving Absolute-Value Inequalities

Front

What is an absolute value inequality?

Back

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

Front

How do you solve the inequality |x| < a?

Back

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

Front

How do you solve the inequality |x| > a?

Back

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

Front

What does the inequality |2w - 1| < 11 represent?

Back

It represents the values of w that are within 11 units from the point 0.5 on the number line.

Front

Solve the inequality |2w - 1| < 11.

Back

−5 < w < 6.

Front

What does the inequality |x + 3| > -8 imply?

Back

Since absolute values are always non-negative, this inequality is true for all real numbers.

Front

Solve the inequality |x + 3| > -8.

Back

All real numbers.

Front

What does the inequality |2x + 13| < 15 represent?

Back

It represents the values of x that are within 15 units from -13 on the number line.

Front

Solve the inequality |2x + 13| < 15.

Back

−14 < x < 1.

Front

What does the inequality |x - 2| > 3 represent?

Back

It represents the values of x that are more than 3 units away from 2 on the number line.