Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An inequality that involves the absolute value of a variable expression, indicating the distance of the expression from zero on a number line.

Front

How do you solve an absolute value inequality of the form |x| < a?

Back

Split the inequality into two separate inequalities: -a < x < a.

Front

How do you solve an absolute value inequality of the form |x| > a?

Back

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

Front

What does the solution |x - 4| > 5 represent?

Back

It represents the values of x that are more than 5 units away from 4 on the number line.

Front

What is the solution to the inequality |x + 2| < 3?

Back

-5 < x < 1.

Front

What does the solution |x - 1| ≥ 4 represent?

Back

It represents the values of x that are at least 4 units away from 1 on the number line.

Front

How do you interpret the solution p ≤ -13 or p ≥ 7?

Back

It means p can take any value less than or equal to -13 or any value greater than or equal to 7.

Front

What is the solution to the inequality |x + 4| + 8 > 2?

Back

All real numbers.

Front

What is the first step in solving |x - 3| < 2?

Back

Set up the two inequalities: -2 < x - 3 < 2.

Front

What is the solution to the inequality |c + 4| < 5?

Back

-9 < c < 1.