Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

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

Back

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

Front

What does the expression |x - c| < d represent?

Back

It represents the values of x that are within a distance d from c on the number line.

Front

What does the expression |x - c| > d represent?

Back

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

Front

What is the first step in solving the inequality | -8x | < 8?

Back

The first step is to separate it into two inequalities: -8x < 8 and -8x > -8.

Front

How do you interpret the solution x < 8 and x > 0?

Back

This means that x can take any value between 0 and 8, not including 0 and 8.

Front

What is the significance of the 'and' in the solution of an absolute value inequality?

Back

The 'and' indicates that both conditions must be satisfied simultaneously.

Front

What is the significance of the 'or' in the solution of an absolute value inequality?

Back

The 'or' indicates that at least one of the conditions must be satisfied.

Front

How do you graph the solution of an absolute value inequality?

Back

You graph the solution on a number line, shading the appropriate regions based on the solution set.