Question

Evaluate the following: $\left| {13 - 5} \right| - \left| { - 9} \right|$

Answer 1

Hint: The addition is the sum of given two or more than two numbers, or variables and in addition, if we sum the two or more numbers then we obtain a new frame of the number will be found which can be expressed in the form of $ + $ , also in subtraction which is the minus of given two or more than two numbers, but here comes with the condition that in subtraction the greater number sign represented in the number will stay constant example $2 - 3 = - 1$ .

Complete step by step solution:
The given term is the form of modulus concept which can be represented in the form of $\left| {} \right|$
The concept of the modulus is all about the positive numbers like if we take out the given positive numbers from the modulus like $\left| 1 \right| = 1$ it will again get the positive number. Also, if we take out the negative numbers from the modulus bracket them, we also get the positive numbers like $\left| { - 1} \right| = 1$ .
Thus, using this concept, we get, $\left| {13 - 5} \right| - \left| { - 9} \right| = \left| {13 - 5} \right| - 9$ where $\left| { - 9} \right| = 9$ .
Using the subtraction operation, we have $13 - 5 = 8$ and hence we get $\left| 8 \right| - 9$ again by using the modulus we get $8 - 9$ and thus using the simple subtraction we get $8 - 9 = - 1$ which is the required answer.

Note: The modulus concept that we have used in the above problem is known as absolute value. We have studied about integers where we have numbers like $..., - 3, - 2, - 1,0,1,2,3,...$ as we can see that we have both positive and negative numbers so these are the best numbers to explain about absolute values let us take one negative value and one positive value $ - 5$ and $7$ then the absolute values of these two numbers will be $\left| { - 5} \right| = 5$ and $\left| 7 \right| = 7$ as we can see that even the negative integer becomes positive. Thus, the absolute value of an integer is nothing but the integer irrespective of their signs.