How do you simplify $| 33 |$ $abs(33)$ ?

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How do you simplify $| 33 |$ $abs(33)$ ?

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Answer 1 · 2015-08-03T02:17:22

$| 33 | = 33$ $abs(33) = 33$

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 $x \geq 0$ $x>=0$ then $| x | = x$ $abs(x) = x$
if $x < 0$ $x<0$ then $| x | = - x$ $abs(x) = -x$

so for our example $33 \geq 0$ $33>=0$ so
$| 33 | = 33$ $abs(33) = 33$

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.

$| 5 | = 5$ $abs(5) = 5$ because +5 is 5 away from zero
$| - 5 | = 5$ $abs(-5) = 5$ because -5 is 5 away from zero

and this is simplification makes us happy.

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How do you simplify $| 33 |$ $abs(33)$ ?

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How do you simplify $| 33 |$ $abs(33)$ ?