Absolute Value Equations and 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. For example, |-3| = 3 and |3| = 3.

Front

How do you solve an absolute value equation like |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What does it mean when |x| < a?

Back

It means that x is within a distance of a from zero. This can be expressed as -a < x < a.

Front

What does it mean when |x| > a?

Back

It means that x is more than a distance of a from zero. This can be expressed as x < -a or x > a.

Front

Solve the equation |x - 4| = 2.

Back

x - 4 = 2 or x - 4 = -2. So, x = 6 or x = 2.

Front

What is the solution to |x + 3| < 5?

Back

-5 < x + 3 < 5, which simplifies to -8 < x < 2.

Front

What is the solution to |2x - 1| ≥ 3?

Back

2x - 1 ≥ 3 or 2x - 1 ≤ -3. So, x ≥ 2 or x ≤ -1.

Front

What is the absolute value of |-7|?

Back

The absolute value of |-7| is 7.

Front

How do you graph an absolute value inequality like |x| < 4?

Back

You would graph the interval (-4, 4) on a number line.

Front

What does the equation |x| = 0 mean?

Back

It means that x is exactly 0.