# A Guide to the GRE/Absolute Value

# Absolute Value[edit]

The concept of **absolute value** - meaning a number's distance from zero - is tested on nearly every GRE.

## Rule[edit]

**Absolute value makes a negative positive, but otherwise does nothing.**

“| |” designates absolute value. For example, if | *x* + 3 | = 5, there are two possible values for *x*:

*x*+ 3 = 5, meaning*x*is 2*x*+ 3 = -5, meaning*x*is -8

On an absolute value questions, split the value into two equations as seen above.

## Practice[edit]

1. If | 3*x* - 4 | = 5, then what could be the value of *x*?

2. If | *a* | > *a*, then what is the greatest integer that *a* could be?

3. If 3|4*k* - 2| - 12 = -3, what is the value of *k*?

## Comments[edit]

Absolute value tends to be tested in the quantity comparison section of the test, often with a variable modified by a constant within the absolute value. (e.g. | *q* + 7 | = 5) Solve these by writing out both of the potential values for the variable, and *remember that either one could be the value.* For example, in the prior equation, *q* could equal either -2 or -12, so it is unclear whether it is greater or less than -5.

## Answers to Practice Questions[edit]

1. 3,

If | 3*x* - 4 | = 5 then

3*x* - 4 = 5

- or

3*x* - 4 = -5

3*x* - 4 = 5

- Take the first equation and solve it. First, add 4 to both sides.

3*x* = 9

- Now divide both sides by 3.

*x* = 3

*x*is equal to 3. But remember, this is just*one*solution - you still need to solve the other equation.

3*x* - 4 = -5

- Now take the second equation and solve it. Add 4 to both sides.

3*x* = -1

- Now divide both sides by 3.

*x* =

*x*is equal to negative one third.

This means that *x* = 3 *or*

2. -1

Absolute value makes a positive negative, but otherwise does nothing - if the absolute value of a number is greater than that number itself, the number must be negative. The greatest negative number is -1.

3. *k* = 5/4,

If 3|4*k* - 2| - 12 = -3, then

3|4*k* - 2| = 9

- Add 12 to both sides.

|4*k* - 2| = 3

- Divide both sides by 3.

4*k* - 2 = 3

Split both possibilities.

4*k* - 2 = -3

- Add 2 to to both sides

4*k* = 5 .

- Divide both sides by 5.

*k* =