Determining the Sign (positive or negative) of Absolute Value Expressions

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

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

EXAMPLES:

Question: Suppose that

$\,x\,$ is negative. Then, $\,-x\,$ is:

Solution: POSITIVE
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!

Question: Suppose that

$\,x\,$ is positive. Then, $\,-|2x|\,$ is:

Solution: NEGATIVE
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 $\,-1\,$.

Question: Suppose that

$\,x\,$ is negative. Then, $\,|-x|\,$ is:

Solution: POSITIVE
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.

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Solving Simple Absolute Value Sentences

(an even number, please)