Absolute Value 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 inequality?

Back

To solve an absolute value inequality, you can split it into two separate inequalities, one for the positive case and one for the negative case.

Front

What does the inequality |x| < a represent?

Back

It represents the values of x that are within a distance a from 0, meaning -a < x < a.

Front

What does the inequality |x| > a represent?

Back

It represents the values of x that are more than a distance a from 0, meaning x < -a or x > a.

Front

Solve: |x - 2| < 5

Back

-3 < x < 7.

Front

Solve: |x + 1| > 4

Back

x < -5 or x > 3.

Front

What is the first step in solving |x - 3| > 6?

Back

Split into two inequalities: x - 3 > 6 or x - 3 < -6.

Front

Solve: |2x + 1| ≤ 3

Back

-2 ≤ 2x ≤ 2, which simplifies to -1 ≤ x ≤ 1.

Front

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

Back

The solution set is (-2, 2).

Front

What is the solution set for |x| > 3?

Back

The solution set is (-∞, -3) ∪ (3, ∞).