Evaluate the mathematical expression :
\[\left| {35 - 41} \right| - \left| {7 - \left( { - 2} \right)} \right|\]

Hint: Here we need to calculate the value of the given mathematical expression. The modulus is used in the given expression, so we will use the fact that the modulus always gives a positive value irrespective of the input value. We will first evaluate the terms inside the modulus by using basic mathematical operations like addition and subtraction. Then we will remove the modulus and simplify further to find the required answer.

Complete step-by-step answer:
The given mathematical expression is \[\left| {35 - 41} \right| - \left| {7 - \left( { - 2} \right)} \right|\].
We will first evaluate the terms inside the modulus.
Now, we will subtract the terms inside the modulus. Therefore, we get
\[\left| {35 - 41} \right| - \left| {7 - \left( { - 2} \right)} \right| = \left| { - 5} \right| - \left| {7 + 2} \right|\]
On adding the numbers inside the modulus, we get
\[ \Rightarrow \left| {35 - 41} \right| - \left| {7 - \left( { - 2} \right)} \right| = \left| { - 5} \right| - \left| 9 \right|\]
We know from the property of modulus that the modulus always gives a positive value. So \[ - 5\] will become 5 and 9 will remain the same.
\[ \Rightarrow \left| {35 - 41} \right| - \left| {7 - \left( { - 2} \right)} \right| = 5 - 9\]
Now, we will subtract the number 9 from the number 5. Therefore, we get
\[ \Rightarrow \left| {35 - 41} \right| - \left| {7 - \left( { - 2} \right)} \right| = - 4\]
Hence, the required value of the given mathematical expression is equal to \[ - 4\].

Note: A modulus function is defined as the function which gives the absolute value of a variable or a number. It gives only the magnitude of a given number or a variable. The other name of the modulus function is absolute value function. Here, we can make mistakes by not converting the negative number into positive while removing modulus. This will give us the wrong answer. Also, we must not write out the result \[ - 4\] as 4 because the modulus sign is removed before calculating the answer.