Negative Sign Outside Absolute Value
A negative sign outside an absolute value symbol means taking the opposite of the absolute value, written as -|x| = -(|x|). Treat the absolute value symbols like parentheses: first find the absolute value inside, then apply the negative sign to the result. For -|14|: |14| = 14, then apply the negative to get -14. For -|-5|: |-5| = 5, then apply the negative to get -5. Since absolute value is always non-negative, -|x| is always zero or negative. This concept from Reveal Math, Course 1, Module 4 is a key 6th grade algebra skill.
Key Concepts
A negative sign outside an absolute value symbol represents the opposite of that absolute value.
$$ |x| = (|x|)$$.
Common Questions
What does a negative sign outside absolute value mean?
The negative sign represents the opposite of the absolute value. You first find the absolute value (always positive or zero), then take its opposite.
Evaluate -|14|.
First, |14| = 14. Then apply the negative: -|14| = -14.
Evaluate -|-5|.
First, |-5| = 5 (absolute value is always positive). Then apply the negative: -|-5| = -5.
Can -|x| ever be positive?
No. Since |x| is always zero or positive, multiplying by -1 makes the result zero or negative. The only way -|x| = 0 is if x = 0.
What is the order of operations with absolute value and a negative sign?
Treat absolute value bars like parentheses. Evaluate what is inside first (the absolute value), then apply any operations outside, such as multiplying by -1.
When do 6th graders learn about negative signs with absolute value?
Module 4 of Reveal Math, Course 1 covers this in the Integers, Rational Numbers, and Coordinate Plane unit.