Absolute Value Inequalities

Front

What is the definition of 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 of the form |x| < a?

Back

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

Front

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

Back

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

Front

What does the inequality |x - 2| > 3 represent?

Back

It represents two conditions: x - 2 > 3 or x - 2 < -3.

Front

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

Back

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

Front

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

Back

x < -1 or x > 9.

Front

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

Back

It represents two separate regions on the number line: all values less than -1 and all values greater than 2.

Front

What is the first step in solving |x + 3| = 7?

Back

Set up two equations: x + 3 = 7 and x + 3 = -7.

Front

What is the solution to the inequality |x| < 4?

Back

-4 < x < 4.

Front

What does the inequality |x - 5| < 2 mean?

Back

It means that x is within 2 units of 5, or 3 < x < 7.