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, isolate the absolute value expression and then split it into two separate inequalities based on the inequality sign.

Front

What does |x - a| < b represent?

Back

It represents the values of x that are within b units of a on the number line.

Front

What does |x - a| > b represent?

Back

It represents the values of x that are more than b units away from a on the number line.

Front

Solve: |x - 3| < 5

Back

-2 < x < 8.

Front

Solve: |x + 1| > 4

Back

x < -5 or x > 3.

Front

What is the first step in solving |2x - 4| < 6?

Back

Isolate the absolute value by adding 4 to both sides: |2x - 4| < 6.

Front

What is the solution to |x| < 3?

Back

-3 < x < 3.

Front

What is the solution to |x| > 5?

Back

x < -5 or x > 5.

Front

What does the compound inequality x < -1 or x > 2 represent?

Back

It represents values of x that are either less than -1 or greater than 2.