Absolute Value Inequalities Review

Front

What is an absolute value inequality?

Back

An inequality that contains an absolute value expression, representing the distance of a number from zero on the number line.

Front

What does |x - a| < b represent?

Back

The values of x that are within a distance b from a on the number line.

Front

What does |x - a| > b represent?

Back

The values of x that are more than a distance b from a on the number line.

Front

What is the first step in solving |x - 2| < 7?

Back

Set up the compound inequality: -7 < x - 2 < 7.

Front

How do you solve |x - 2| < 7?

Back

Split into two inequalities: x - 2 < 7 and x - 2 > -7, then solve for x.

Front

What is the solution to |x - 2| < 7?

Back

-5 < x < 9.

Front

What is the first step in solving |x - 2| > 7?

Back

Set up the compound inequality: x - 2 < -7 or x - 2 > 7.

Front

How do you solve |x - 2| > 7?

Back

Split into two inequalities: x - 2 < -7 or x - 2 > 7, then solve for x.

Front

What is the solution to |x - 2| > 7?

Back

x < -5 or x > 9.

Front

What is an AND compound inequality?

Back

An inequality that requires both conditions to be true simultaneously.