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 |x + 4| < 2 represent?

Back

It represents the values of x that are within 2 units of -4 on the number line.

Front

Solve the inequality |10 + 4x| < 14.

Back

x < 1 and x > -6.

Front

Solve the inequality |3x - 9| < 3.

Back

2 < x < 4.

Front

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

Back

It implies that all real numbers satisfy the inequality since absolute values are always non-negative.

Front

Solve the inequality |x + 1| ≥ 3.

Back

x ≤ -4 or x ≥ 2.

Front

What is the solution set for |x| < 5?

Back

The solution set is -5 < x < 5.

Front

What is the solution set for |x| > 3?

Back

The solution set is x < -3 or x > 3.