Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which measures the distance of a number from zero on the number line.

Front

How do you solve the inequality |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

How do you solve the inequality |x| > a?

Back

To solve |x| > a, split it into two inequalities: x < -a or x > a.

Front

What does the expression |x - c| ≤ d represent?

Back

It represents the set of all x values that are within a distance d from c on the number line.

Front

What does the expression |x - c| ≥ d represent?

Back

It represents the set of all x values that are at least a distance d away from c on the number line.

Front

Solve: |x + 2| < 3

Back

-5 < x < 1

Front

Solve: |2x - 4| > 6

Back

x < -1 or x > 5

Front

What is the graphical representation of |x| < a?

Back

It is represented by an open interval on the number line from -a to a.

Front

What is the graphical representation of |x| > a?

Back

It is represented by two rays extending from -∞ to -a and from a to ∞ on the number line.

Front

Solve: 3|x - 1| + 2 < 11

Back

x < 4 or x > -2/3