Question

How do you simplify the expression $-\left| -13 \right|$?

Answer 1

The modulus function gives the absolute value of the term present inside it. In other words, $\left| a \right|$ gives non-negative value as output always.
The modulus function $\left| a \right|=a$, if $a>0$ , and $\left| a \right|=-a$ if $a<0$. We will use this definition of the function to simplify the given term.

Complete step by step answer:
We are given the expression $-\left| -13 \right|$, as we can see that it has a modulus function. To simplify the given expression, we first have to evaluate the modulus function.
The modulus function is $\left| -13 \right|$. We know that the modulus function $\left| a \right|=a$, if $a>0$ , and $\left| a \right|=-a$ if $a<0$. Here, $a=-13$, that is $a<0$. As the term inside the modulus function is a negative quantity, the value of the modulus function is,
$\Rightarrow \left| -13 \right|=-\left( -13 \right)$
Multiplying $-13$ by $-1$, we get $13$. substituting this value above,
$\Rightarrow \left| -13 \right|=13$
Now that we have evaluated the modulus function, we can evaluate the given expression. As follows,
$-\left| -13 \right|$
Substituting the value of the modulus function, we get
$\Rightarrow -\left| -13 \right|=-\left( 13 \right)$
Multiplying $13$ by $-1$, we get $-13$. substituting this value above
$\Rightarrow -\left| -13 \right|=-13$
Hence, the value of the given expression is 13.

Note:
To solve questions based on the modulus, one should remember the properties of the modulus function. Some of the important properties are given below,
$\left| x \right|$ is always gives a non-negative output, that is $\left| x \right|\ge 0$.
If we are given that $\left| x \right|=a$, then $x=\pm a$.
If we are given that $\left| x \right|If we are given that \[\left| x \right|>a$, then $x<-a$ or $x>a$.