Absolute Value Inequalities Review

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 write the absolute value inequality |x| < a?

Back

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

Front

How do you write the absolute value inequality |x| > a?

Back

This inequality means that x is either less than -a or greater than a, or x < -a or x > a.

Front

What does the symbol ≤ mean in an inequality?

Back

It means 'less than or equal to'.

Front

What does the symbol ≥ mean in an inequality?

Back

It means 'greater than or equal to'.

Front

What is the first step in solving the inequality |x - 3| < 5?

Back

Get the absolute value alone by isolating it on one side of the inequality.

Front

What is the solution to the inequality |x - 3| < 5?

Back

The solution is -2 < x < 8.

Front

What does it mean to graph an inequality with a closed dot?

Back

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

Front

What does it mean to graph an inequality with an open dot?

Back

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

Front

When graphing the solutions to 'AND' inequalities, how does the shading appear?

Back

The shading overlaps between the two inequalities, indicating the intersection of the solution sets.