Solving Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

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

Split into two inequalities: -a < x < a.

Front

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

Back

Split into two inequalities: x < -a or x > a.

Front

What does the inequality |x - c| < d represent?

Back

The values of x that are within d units of c on the number line.

Front

What does the inequality |x - c| > d represent?

Back

The values of x that are more than d units away from c on the number line.

Front

What is the solution to |x + 3| > -8?

Back

All real numbers, since absolute values are always non-negative.

Front

What is the solution to |5x| > 30?

Back

x < -6 or x > 6.

Front

What is the solution to |x - 6| > 4?

Back

x < 2 or x > 10.

Front

What is the solution to |12 + w| ≥ -5?

Back

All real numbers, since absolute values are always non-negative.

Front

What is the solution to |d + 1| - 7 ≥ -1?

Back

d ≤ -3 or d ≥ 1.