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 split it into two separate inequalities: one for the positive case and one for the negative case.

Front

Solve: |x - 2| < 5

Back

-3 < x < 7

Front

What does the inequality |x| > a represent?

Back

It represents two cases: x > a or x < -a.

Front

Solve: |x + 1| ≥ 4

Back

x ≤ -5 or x ≥ 3

Front

What is the first step in solving |3x - 6| < 9?

Back

Get the absolute value alone by adding 6 to both sides.

Front

Solve: 2|x - 3| + 4 > 10

Back

x < 1 or x > 5

Front

What does the solution x > 5 or x < -11 indicate?

Back

It indicates that x can be any number greater than 5 or any number less than -11.

Front

Solve: |2x + 3| - 5 < 0

Back

No solution, since absolute values are always non-negative.

Front

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

Back

It is represented by an open interval (-a, a) on the number line.