Absolute Value Equations & 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

What does the symbol '|' represent in mathematics?

Back

The symbol '|' represents absolute value.

Front

What is the solution set for the absolute value equation |x| = a (where a > 0)?

Back

The solution set is x = a or x = -a.

Front

What is the solution set for the absolute value inequality |x| < a (where a > 0)?

Back

The solution set is -a < x < a.

Front

What is the solution set for the absolute value inequality |x| > a (where a > 0)?

Back

The solution set is x < -a or x > a.

Front

When solving the inequality |x| < a, what type of compound inequality is formed?

Back

A compound inequality involving 'and': -a < x < a.

Front

When solving the inequality |x| > a, what type of compound inequality is formed?

Back

A compound inequality involving 'or': x < -a or x > a.

Front

What does an open dot represent when graphing inequalities?

Back

An open dot represents that the endpoint is not included in the solution set, used for < and >.

Front

What does a closed dot represent when graphing inequalities?

Back

A closed dot represents that the endpoint is included in the solution set, used for ≤ and ≥.

Front

How do you graph the inequality x ≤ -2?

Back

You place a closed dot on -2 and shade to the left.