Question

Which sign of the following will come in the space to make the expression true?
 ${\left( { - 6} \right) + \left( { - 5} \right) - 2}\, \_\_\_\_ {\left( { - 6} \right) + \left( { - 5 - 2} \right)}$
A) <
B) >
C) =
D) None of these

Answer 1

Hint:
To solve this problem first we open all the brackets on the left side of the space and solve. Then to solve the right hand side of the brackets we’ll solve the bracket first and then open it. After getting the result from each side we can compare the quantities.

Complete step by step solution:
The given expression here is $\left( { - 6} \right) + \left( { - 5} \right) - 2 = \left( { - 6} \right) + \left( { - 5 - 2} \right)$.
We need to find the sign to be put in the box, which will make the equation true.
To do that, we will solve the LHS and the RHS individually and then compare to get the sign that will make the expression true.
Now, we will solve LHS.
$\therefore $ Left-hand side $ = \left( { - 6} \right) + \left( { - 5} \right) - 2$
$=-6-5-2 \\
=-13$
Then, we will solve RHS.
$\therefore $ Right-hand side $ = \left( { - 6} \right) + \left( { - 5 - 2} \right)$
$ = - 6 + \left( { - 7} \right)$
$=-6-7 \\
=-13$
Here, we can now observe that on solving LHS and RHS individually, we get LHS = RHS.
So, the sign in the box must be = sign to make the expression true.
 $\therefore \left( { - 6} \right) + \left( { - 5} \right) - 2 = \left( { - 6} \right) + \left( { - 5 - 2} \right)$

Thus, option (C) is the correct answer.

Note:
Arithmetic is a branch of mathematics that deals with the numbers and their operations such as addition, subtraction, multiplication, division, etc.
Summation or subtraction of two numbers is dependent on the signs of the numbers. If signs of both the numbers are the same, then addition is done and the result will have the same sign as the numbers had and if the signs of the numbers are different, then subtraction is done and the result will have the sign of the greater number taken without sign.
For example, in the expression -6-4 or 4+2 , addition will take place as the signs are same and the sign of the result will be same as the sign of both numbers and in the expression -6+3 , subtraction will take place as the signs of both numbers are different and the result will have a negative sign as the greater number taken without sign is 6 and it has a negative sign.