Distance from Zero

The absolute value of a number is its distance from zero on the number line, with no sign: |3| = 3 and |-3| = 3, because 3 and -3 are both three steps from zero. Distance is never negative, so an absolute value is never negative.

3 and -3 are both three steps from 0: |3| = |-3| = 3

Inside the bars, arithmetic happens first: |2 - 7| = |-5| = 5. The bars are like brackets that also throw the sign away at the end. Two different numbers share every absolute value except zero: |0| = 0 and nothing else has absolute value 0.