Math 1 · Lesson 7 · part 2 of 7
Absolute value means distance from zero
The two bars around a number ask one question: how far is this from zero?
Absolute value means distance from zero
The two bars around a number ask one question: how far is this from zero? They never ask which direction. So |5| = 5, because 5 is five steps to the right of zero, and |−5| = 5, because −5 is five steps to the left. A distance is never negative.
That is why an absolute value sentence always talks about two places at once. If |x| = 5, then x is five steps from zero, and there are two such numbers: 5 and −5. Every absolute value inequality in this lesson turns into two ordinary inequalities for the same reason.