Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An inequality that involves the absolute value of a variable expression, indicating the distance of the expression from zero on a number line.

Front

What does |x - a| > b represent?

Back

It represents the values of x that are more than b units away from a on the number line.

Front

What does |x - a| < b represent?

Back

It represents the values of x that are less than b units away from a on the number line.

Front

Is |x - 2| > 3 an 'and' or 'or' problem?

Back

It is an 'or' problem.

Front

Is |x - 6| < 4 an 'and' or 'or' problem?

Back

It is an 'and' problem.

Front

What is the first step to solve |2x + 12| < 8?

Back

Split into two inequalities: 2x + 12 < 8 and 2x + 12 > -8.

Front

How do you isolate the absolute value in |x - 5| = 3?

Back

You can isolate it by adding or subtracting the constant from both sides.

Front

What is the solution set for |x - 3| > 5?

Back

x < -2 or x > 8.

Front

What is the solution set for |x + 4| < 2?

Back

-6 < x < -2.

Front

What is the first step to solve |x - 2| > 3?

Back

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