Absolute Value Inequalities Review

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

What does the inequality |x| < a represent?

Back

It represents the set of numbers x that are within a distance a from 0 on the number line.

Front

What does the inequality |x| > a represent?

Back

It represents the set of numbers x that are more than a distance a from 0 on the number line.

Front

How do you solve the inequality |2x + 12| < 8?

Back

Split into two inequalities: 2x + 12 < 8 and 2x + 12 > -8.

Front

What is the first step in solving |x - 5| ≤ 3?

Back

Split into two inequalities: x - 5 ≤ 3 and x - 5 ≥ -3.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities using 'and' or 'or'.

Front

What does 'AND' mean in a compound inequality?

Back

It means both conditions must be true at the same time.

Front

What does 'OR' mean in a compound inequality?

Back

It means at least one of the conditions must be true.

Front

When do you use a closed dot on a number line?

Back

Use a closed dot for inequalities with ≤ or ≥, indicating that the endpoint is included.

Front

When do you use an open dot on a number line?

Back

Use an open dot for inequalities with < or >, indicating that the endpoint is not included.