Absolute Value Equations and 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 always non-negative.

Front

Solve for x: |x| = 5

Back

x = 5 or x = -5

Front

What does the inequality |x| < a represent?

Back

It represents all numbers x that are within a distance a from 0 on the number line.

Front

Solve for x: |x - 3| < 4

Back

-1 < x < 7

Front

What does the inequality |x| > a represent?

Back

It represents all numbers x that are more than a distance a from 0 on the number line.

Front

Solve for x: |2x + 1| = 3

Back

x = 1 or x = -2

Front

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

Back

No solution, because absolute values cannot be negative.

Front

When graphing |x| < a, what type of circle is used?

Back

An open circle is used.

Front

What is the solution to the inequality |x - 5| ≥ 2?

Back

x ≤ 3 or x ≥ 7

Front

Solve for x: |x + 2| + 3 = 0

Back

No solution, because absolute values cannot be negative.