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 |3x + 6| ≥ 15 represent?

Back

It represents values of x that are either greater than or equal to 15 units away from -6.

Front

Solve the inequality |3x + 6| ≥ 15.

Back

x ≤ -7 or x ≥ 3.

Front

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

Back

It represents values of x that are within 15 units of -13.

Front

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

Back

x < 1 and x > -14.

Front

What is the first step in solving the inequality -5|x - 4| > -20?

Back

Divide both sides by -5, remembering to reverse the inequality sign.

Front

Solve the inequality -5|x - 4| > -20.

Back

x < 8 and x > 0.

Front

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

Back

It represents values of w that are within 11 units of 0.5.