Absolute Value Inequalities

Front

Define 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

What does the inequality |x| < a represent?

Back

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

Front

What does the inequality |x| ≥ a represent?

Back

It represents the set of all numbers x that are at least a distance a from 0 on the number line.

Front

Solve: |x + 2| < 3

Back

-5 < x < 1

Front

Solve: |x - 1| ≥ 4

Back

x ≤ -3 or x ≥ 5

Front

What is the first step in solving an absolute value inequality?

Back

Isolate the absolute value expression on one side of the inequality.

Front

Solve: |3x - 6| < 9

Back

-1 < x < 5

Front

Solve: |x + 5| ≥ 2

Back

x ≤ -7 or x ≥ -3

Front

What is the difference between |x| < a and |x| ≤ a?

Back

|x| < a means x is strictly within a distance a from 0, while |x| ≤ a includes the endpoints.

Front

Solve: |2x + 3| < 7

Back

-5 < x < 2