Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

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

Front

What does |x| > a mean?

Back

It means that x is either greater than a or less than -a.

Front

What does |x| < a mean?

Back

It means that x is between -a and a, or -a < x < a.

Front

How do you solve |x - 2| > 3?

Back

Separate into two inequalities: x - 2 > 3 or x - 2 < -3.

Front

How do you solve |x - 2| < 3?

Back

Separate into one compound inequality: -3 < x - 2 < 3.

Front

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

Back

Separate into two inequalities with an 'and': -8x < 8 and -8x > -8.

Front

What does the solution x < -3 and x > -4 represent?

Back

It represents a range of values for x that satisfy both conditions.

Front

What is a compound inequality?

Back

An inequality that combines two inequalities, often using 'and' or 'or'.

Front

What does 'and' mean in inequalities?

Back

Both conditions must be true at the same time.

Front

What does 'or' mean in inequalities?

Back

At least one of the conditions must be true.