Absolute Value Inequalities

Front

What is 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 can split it into two separate inequalities, one for the positive case and one for the negative case.

Front

What does the inequality |x| < a represent?

Back

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

Front

What is the first step in solving |x - 3| < 5?

Back

Split it into two inequalities: -5 < x - 3 < 5.

Front

What is the solution to the inequality |x + 2| > 3?

Back

x < -5 or x > 1.

Front

How do you graph the solution of |x| < 4?

Back

Draw a number line and shade the region between -4 and 4, not including the endpoints.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.

Front

What is the solution to the inequality |2x - 6| < 8?

Back

-1 < x < 7.

Front

What is the solution to the inequality |x - 1| > 3?

Back

x < -2 or x > 4.