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 of the form |x| < a?

Back

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

Front

How do you solve an absolute value inequality of the form |x| > a?

Back

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

Front

What does it mean if an absolute value inequality has no solution?

Back

It means that there are no values of x that satisfy the inequality, often occurring when the inequality is set to a negative number.

Front

Solve: |x - 5| < 3

Back

2 < x < 8.

Front

Solve: |x + 2| > 4

Back

x < -6 or x > 2.

Front

What is the solution to |x| = 0?

Back

The solution is x = 0.

Front

How do you interpret the inequality |x + 1| < 5 graphically?

Back

It represents all points on the number line that are within 5 units of -1.

Front

Solve: 2|x - 3| - 4 < 0

Back

x < 2.

Front

What is the solution to |2x + 1| = 3?

Back

x = 1 or x = -2.