Question

Explain the difference in meaning between |-3| and -3. In your explanation, be sure to include various key words you learned within this unit.

Answer 1

on number line |-3| is 3 units right of zero
but
-3 is 3 units left of zero
so the difference is 6 units.

Answer 2

The difference in meaning is that

-3 is a signed value. It lies to the left of zero

+3 is also a signed value, and since it is positive, it lies to the right of zero

|-3| is just the physical distance (left or right) of -3 from zero. Since we live in a physical world, all distances are positive, so its signed value is 3.

Since +3 is also 3 units from zero, |+3| = 3

|-3| = |+3| = 3 since both are three units away from zero.

So, when using absolute values as numbers, rather than distances,

|x| = x if x is not negative
|x| = -x if x is negative