Absolute Value Inequalities Review

Front

What is an absolute value inequality?

Back

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

Front

What does the symbol '≤' indicate in an inequality?

Back

It indicates that the value can be less than or equal to a certain number.

Front

What does the symbol '≥' indicate in an inequality?

Back

It indicates that the value can be greater than or equal to a certain number.

Front

What is a compound inequality?

Back

An inequality that combines two or more inequalities, often 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, creating a range of values.

Front

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

Back

You use 'or' when the absolute value expression is greater than a number, indicating two separate ranges.

Front

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

Back

Split it into two inequalities: -a < x < a.

Front

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

Back

Split it into two inequalities: x < -a or x > a.

Front

What is the first step in solving |2x - 3| ≤ 7?

Back

Add 3 to both sides, then divide by 2 to isolate x.

Front

What is the solution set for the inequality |x| ≤ 4?

Back

-4 ≤ x ≤ 4.