Absolute Value Inequalities

Front

What is absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you solve an absolute value inequality?

Back

To solve an absolute value inequality, you split it into two separate inequalities: one for the positive case and one for the negative case.

Front

What does |x + 3| > 8 represent?

Back

It represents two inequalities: x + 3 > 8 or x + 3 < -8.

Front

What is the solution to |x + 3| > 8?

Back

x > 5 or x < -11.

Front

What does |x - 4| < 5 represent?

Back

It represents the compound inequality: -5 < x - 4 < 5.

Front

What is the solution to |x - 4| < 5?

Back

The solution is -1 < x < 9.

Front

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

Back

The first step is to divide both sides by -5, which reverses the inequality.

Front

What is the solution to -5|x - 4| > -20?

Back

The solution is x < 8 and x > 0.

Front

What does the compound inequality m < -1 OR m > 2 mean?

Back

It means that m can be any value less than -1 or any value greater than 2.

Front

How do you graph the solution to an absolute value inequality?

Back

You graph the critical points and shade the regions that satisfy the inequality.