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

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

Front

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

Back

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

Front

What does the inequality |y - 4| ≥ 8 represent?

Back

It represents that the distance between y and 4 is greater than or equal to 8.

Front

What is the first step in solving |y - 4| ≥ 8?

Back

Separate into two inequalities: y - 4 ≥ 8 or y - 4 ≤ -8.

Front

Solve the inequality |c + 4| < 5.

Back

-9 < c < 1.

Front

What is the first step in solving | -8x | < 8?

Back

Separate into two inequalities with an 'and': -8 < 8x < 8.

Front

How do you interpret the solution y ≤ -4 or y ≥ 12?

Back

It means y is either less than or equal to -4 or greater than or equal to 12.

Front

What is the solution to the inequality 6 - 2|m - 3| > -4?

Back

-2 < m < 8.

Front

What does the inequality |x - 3| < 2 mean?

Back

It means the distance between x and 3 is less than 2.