On average you will see at least one question on the Revised GRE dealing with absolute values. You may even see a few. Yet, absolute value gets lost in the prep fray amongst the more popular concepts. So if you don’t want this relatively innocuous concept to surprise you test day read on.
For positive numbers finding the absolute value is easy — it is always the number between the absolute value signs, which look like this
When we take the absolute value of a negative number, we drop the negative, and the absolute value sign.
What is the value of x in the equation
Now take a look at the following:
Anything seem off? Well, the absolute value of any number can never be a negative therefore there is no value for
To solve for a variable inside an absolute value sign, we want to remove the absolute value sign and solve the equation. However, there is a slight twist: you will want to create two separate equations. For one remove the absolute value signs and solves for
Our two equations are:
If this seems strange, think of it this way: when you find a value for
Now let’s complicate things a little and throw an inequality in to the picture. Have a look:
We turn the inequality sign into an equal sign and solve for
However, when we turn