Question

How do you simplify $ - | - 33|$ ?

Answer 1

Hint: The given expression has an absolute value bracket within it. First, solve the inside of the absolute value bracket and then the outside part. The absolute value brackets make any negative value positive and any positive value positive itself. So first convert the negative value inside the absolute value bracket positive and then evaluate the remaining expression.

Complete step-by-step answer:
Firstly, the absolute value bracket converts a negative value within it to a positive and a positive value returns itself.
The given expression, $ - | - 33|$
On solving the expression inside the absolute value bracket first, i.e., converting negative value to positive value,
We get,
$ \Rightarrow - |33|$
Whenever you convert a negative value into a non-negative value inside the absolute value brackets,
Do not forget to write the non-negative value back into the absolute value brackets.
$ \Rightarrow | - 33| \Leftrightarrow |33|$
Now, there is a positive value inside the absolute value bracket, so it returns itself.
We get,
$ \Rightarrow - 33$
$\therefore ( - 33)$will be the final answer since we can’t any further solve it.
The absolute value forces the value inside it to be positive and does not affect whatever is outside.
That’s why the outside negative sign remains there itself.

$\therefore - | - 33| = - 33$

Additional information: A mathematical function, absolute value converts any value to non-negative value. Absolute value is also known as the number’s distance from zero. The absolute value of any value is written by using two straight bars and the value within them.

Note:
Always keep in mind that anything outside the absolute value brackets does not affect the values inside the absolute value brackets. Whenever there is an expression with other mathematical functions including the absolute bracket function, solve the absolute value function first. It has more priority than other mathematical functions.