# How do you simplify abs(33)?

Aug 3, 2015

$\left\mid 33 \right\mid = 33$

#### Explanation:

The absolute value function is a special class of function called a piecewise function. What this means is it has more than one definition that depends on the input.

Those definitions are:
if $x \ge 0$ then $\left\mid x \right\mid = x$
if $x < 0$ then $\left\mid x \right\mid = - x$

so for our example $33 \ge 0$ so
$\left\mid 33 \right\mid = 33$

The above is the technical definition of the function. However, I think it is easier to think about it as a distance function. The absolute value tell you how far a number is from zero. Then it becomes obvious what the value should be.

$\left\mid 5 \right\mid = 5$ because +5 is 5 away from zero
$\left\mid - 5 \right\mid = 5$ because -5 is 5 away from zero

and this is simplification makes us happy.