Practice absolute value inequalities and equations

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 all values of x that are within a distance a from 0 on the number line.

Front

What does the inequality |x| > a represent?

Back

It represents all values of x that are more than a distance a from 0 on the number line.

Front

Solve: |x + 3| < 8

Back

-11 < x < 5

Front

Solve: |x - 3| > 8

Back

x > 11 or x < -5

Front

What is the solution to |x + 3| > 8?

Back

x > 5 or x < -11

Front

Solve: |2x + 1| ≤ 19

Back

-10 ≤ x ≤ 9

Front

What is the solution to |x| = a?

Back

x = a or x = -a.

Front

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

Back

|x| < a excludes the endpoints, while |x| ≤ a includes them.

Front

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

Back

It means there are no values of x that satisfy the equation.