Absolute Value Inequalities

Front

Define 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 is an Absolute Value Inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, typically in the form |x| < a, |x| > a, |x| ≤ a, or |x| ≥ a.

Front

Solve: |x| < 5.

Back

-5 < x < 5.

Front

Solve: |x| > 3.

Back

x < -3 or x > 3.

Front

What does |x| = a represent?

Back

It represents two equations: x = a and x = -a.

Front

Solve: |2x - 1| = 7.

Back

x = 4 or x = -3.

Front

What is the solution set for |x + 2| < 0?

Back

No solution, since absolute values cannot be negative.

Front

Solve: 3|x - 1| - 6 < 0.

Back

x < 1.

Front

What is the graphical representation of |x| < a?

Back

A number line showing an open interval from -a to a.

Front

Solve: |x - 3| + 2 > 5.

Back

x < 1 or x > 5.