Question

The value of \[\left| 7 \right| + \left| 5 \right| - \left| 7 \right| - \left| { - 3} \right|\] where \[\left| {} \right|\] is the absolute value of an integer is
A) 0
B) 1
C) 2
D) 3

Answer 1

Hint:
We have to find the absolute value of the given sum only. Absolute value of a number is always the same if the number is positive and if it is negative then it’ll be multiplied by minus sign to make it positive. Ultimately the absolute number of any number is always positive.

Complete step by step solution:
Given that,
\[\left| 7 \right| + \left| 5 \right| - \left| 7 \right| - \left| { - 3} \right|\]
Taking absolute values
\[
   \Rightarrow 7 + 5 - 7 - 3 \\
   \Rightarrow 12 - 10 \\
   \Rightarrow 2 \\
\]

So the correct option is C.

Note:
Absolute value of a number or also known as modulus is the non-negative value of that number.
This is sign of modulus \[ \to \left| {} \right|\]
Absolute value is never negative. Say the absolute value of 5 and -5 both are the same, that is 5. Also note that signs between modulus will remain the same because they are operations rather than only signs of number or modulus of that number is changed.