Question

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

Answer 1

Hint: 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 \[x>a\].