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

What does the inequality |x| < a represent?

Back

It represents the values of x that are within a distance a from 0, meaning -a < x < a.

Front

What does the inequality |x| > a represent?

Back

It represents the values of x that are more than a distance a from 0, meaning x < -a or x > a.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities using 'and' or 'or'.

Front

When do you use 'and' in absolute value inequalities?

Back

You use 'and' when the absolute value expression is less than or equal to a number (|x| ≤ a).

Front

When do you use 'or' in absolute value inequalities?

Back

You use 'or' when the absolute value expression is greater than or equal to a number (|x| ≥ a).

Front

Solve: |p + 3| ≥ 10

Back

p ≤ -13 or p ≥ 7.

Front

Solve: |x + 3| > -8

Back

All real numbers.

Front

What is the solution to |x + 4| - 8 > 2?

Back

x > 6 or x < -14.

Front

What is the solution to |x - 5| < 3?

Back

2 < x < 8.