GMAT Resources

Rules of Absolute Value

Rules of Absolute Value

The concept of absolute value has stumped many test takers over the years. For many students, absolute value is nothing but a positive version of any number. For instance, the absolute value of 3 is 3 and -3 is also 3. While this example is correct, it is better to understand the real definition of absolute value. Absolute value of a number is the distance from zero on the number line. So, in the above example both the numbers are 3 units away from 0 on the number line.

Let’s look at two absolute value rules which will help you on the exam day.

Consider the absolute value equations as two separate equations:

Suppose you are faced with the question – What could be the value of x if

|3x-5| = 10

The two separate equations that can come out of it are:

3x-5= 10

3x-5= -10

Essentially, you are keeping one equation as it is, while the other one is multiplied by -1.

Be careful with inequalities:

Inequalities present a different challenge with absolute values and the duo often appears together in exams.

So if you have an inequality x<3, it means that all the values below 2, 1, 0, -1, -2, -3, -4…satisfy the condition.

However, if the statement is |x|<3, then the case becomes quite different. In this case, while the numbers 2, 1, 0,-1 and -2 will satisfy the condition but -4 will not since the absolute value of -4 becomes 4.

So, if you split the above inequality into two possibilities, you have

x<3 and x>-3

In the exam, be careful to read the question very carefully. Check the positive and negative, split the equation/inequality and then eliminate the value which does not match the answer choices.

Attempt a few questions.

Sign up for our newsletter!

Get expert tips, exam updates and news articles to help improve your test score


Free Prep Classes

Take online classes to learn from the subject experts