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

What does the inequality |x| < a represent?

Back

It represents the values of x that are within a distance a from 0, meaning -a < x < a.

Front

What does the inequality |x| ≤ a represent?

Back

It represents the values of x that are at most a distance a from 0, meaning -a ≤ x ≤ a.

Front

What does the inequality |x| > a represent?

Back

It represents the values of x that are more than a distance a from 0, meaning x < -a or x > a.

Front

What does the inequality |x| ≥ a represent?

Back

It represents the values of x that are at least a distance a from 0, meaning x ≤ -a or x ≥ a.

Front

Solve the inequality |x + 4| ≤ 8.

Back

x ≤ 4 and x ≥ -12.

Front

Solve the inequality |x + 3| > 8.

Back

x > 5 or x < -11.

Front

Solve the inequality |y - 4| ≥ 8.

Back

y ≤ -4 or y ≥ 12.

Front

Solve the inequality |2x + 13| < 15.

Back

x < 1 and x > -14.

Front

Solve the inequality |3x + 6| ≥ 15.

Back

x ≤ -7 or x ≥ 3.