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.