Absolute Value Equations/Inequalites

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 equation |x| = a represent when a < 0?

Back

The equation |x| = a has no solution when a is less than 0, because absolute values cannot be negative.

Front

How do you solve the equation |x| = a when a ≥ 0?

Back

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

Front

What is the solution to the equation |3n + 12| = 2n?

Back

No Solution.

Front

What is the solution to the equation |x + 9| = -5?

Back

No Solution.

Front

What is the solution to the equation |x| = 60?

Back

x = 60 or x = -60.

Front

What is the solution to the equation 3|−8x| + 8 = 80?

Back

x = -3 or x = 3.

Front

What is the solution to the equation |v| = 15?

Back

v = 15 or v = -15.

Front

What does the inequality |x| < a represent?

Back

The inequality |x| < a means that x is between -a and a, or -a < x < a.

Front

What does the inequality |x| > a represent?

Back

The inequality |x| > a means that x is either less than -a or greater than a, or x < -a or x > a.