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 the inequality |x + 4| - 8 > 2 represent?

Back

It represents the values of x that are either greater than 6 or less than -14.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.

Front

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

Back

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

Front

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

Back

Graph the critical points on a number line and shade the appropriate regions based on the inequality.

Front

What is the solution to the inequality |3c - 4| < 12?

Back

The solution is -2 2/3 < c < 5 1/3.

Front

What does the inequality 6 - 2|m - 3| > -4 represent?

Back

It represents the values of m that are between -2 and 8.

Front

What is the solution to the inequality 3 |2x + 7| - 7 < -4?

Back

The solution is x < -3 and x > -4.