Question

The value of $9 + \left| { - 4} \right|$ is equal to
A. 5
B. -5
C. 13
D. -13

Answer 1

Hint: First, find the value of |-4|. As the expression is in the mod, it means it will always give a positive value. So, the value of |-4| will be 4. Now add 9 in the value of |-4|. The output will be the desired result of the expression.

Complete step-by-step solution:
Given: - The expression $9 + \left| { - 4} \right|$.
A modulus function is a function that gives an absolute value to a number or variable. This results in the magnitude of the number of variables. It is often referred to as the function of absolute value. The output of the function is always positive irrespective of the data.
When x is positive, it will return,
$ \Rightarrow $ |x| = x
When x is negative, it will return,
$ \Rightarrow $ |x| = -x
So, it can be redefining the modulus function as,
$f\left( x \right) = \left\{ \begin{array}{l}
x, & if\,x \ge 0\\
 - x, & if\,x < 0
\end{array} \right.$
It means if the value of x is greater than or equal to 0, the function will return the actual value. But if the value of x is less than 0, it will take out the negative sign and return the value.
As we know, $ - 4$ is less than 0. So,
\[ \Rightarrow \left| { - 4} \right| = - \left( { - 4} \right)\]
Simplify the term,
\[ \Rightarrow \left| { - 4} \right| = 4\]
Now add 9 on both sides,
$ \Rightarrow 9 + \left| { - 4} \right| = 9 + 4$
Add the terms on the right side.
$\therefore 9 + \left| { - 4} \right| = 13$

Hence, option (C) is the correct answer.

Note: Whenever we face such types of questions the key concept, we have to remember is that whenever the modulus is applied i.e., the absolute value is taken, positive numbers or integers remain the same, and negative integers or numbers become positive, so first apply the modulus as above applied in the solution part and then simplify according to the above description we will get the required answer.