Absolute Value Equations/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

How do you solve an absolute value equation?

Back

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

Front

What is the solution to the equation |x| = 5?

Back

x = 5 or x = -5.

Front

How do you solve an absolute value inequality?

Back

For |x| < a, solve -a < x < a. For |x| > a, solve x < -a or x > a.

Front

What is the solution to the inequality |x| < 3?

Back

-3 < x < 3.

Front

What is the solution to the inequality |x| > 4?

Back

x < -4 or x > 4.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, perform inverse operations to both sides of the equation until the absolute value expression is alone.

Front

What is the solution to the equation |3 + r| = 7?

Back

r = 4 or r = -10.

Front

What does the inequality |m| + 5 < 9 represent?

Back

It represents the range of values for m that are within 4 units of 0.

Front

What is the solution to the inequality |x + 4| ≤ 2?

Back

-6 ≤ x ≤ -2.