Absolute Value

Definition: (Geometric Version) The absolute value of a real number x, denoted by |x|, is the distance from x to the origin.

Definition: (Algebraic Version) x when AND

–x when < 0

Properties of Absolute Value

1. For all real numbers x, we have

(a)

(b) and

(c)

(d)

2. For all real numbers a and b, we have

(a) and ()

(b) (the triangle inequality)

Distance on a Number Line

For real numbers a and b, the distance between a and b is