# Determining the Sign (Positive or Negative) of Absolute Value Expressions

Want some absolute value instruction and practice without variables first? Simplifying Basic Absolute Value Expressions

In this exercise, you will determine the sign (positive or negative) of simple expressions. Most expressions—but not all—involve absolute values.

Keep in mind that if a number
is *positive* or *negative*,
then it is *nonzero* (not zero).
When a number is nonzero,
then its absolute value—its distance from zero—is
positive.

## Examples

Note:
Remember that
$\,-x\,$ denotes the opposite of $\,x\,.$
If $\,x\,$ is positive,
then its opposite is negative.
If $\,x\,$ is negative,
then its opposite is positive.
*
The presence of a minus sign in front of a
variable does not necessarily mean that you have
a negative number!
*

Note:
In this example, it doesn't matter if
$\,x\,$ is positive or negative.
The expression $\,|2x|\,$ will
*always* be positive,
since it reports a distance from zero.
Then, it is being multiplied by $\,-1\,,$
which gives a negative number.
*
Remember that a minus sign outside the
absolute value indicates multiplication by
* $\,-1\,.$

Note:
In this example, it doesn't matter if
$\,x\,$ is positive or negative.
The expression $\,|-x|\,$ will
*always* be positive,
since it reports a distance from zero.
*
Remember that the absolute value of any
nonzero number is positive.
*