Question

The difference between integers x and -6 is -5. Find the value of x.

Answer 1

Hint: Here we have to find difference or sum of the given data. Here the data is in the form of integers. Where in integers we have both positive and negative numbers. Here the word difference implies we have to do the subtraction arithmetic operation and hence we can determine the value of the unknown.

Complete step-by-step answer:
In mathematics we have 4 kinds of mathematical operations which are implied to the numbers or numerals. They are addition, subtraction, multiplication and division.
Here the starting line of the question is involving the word difference of, the word difference will represent the subtraction arithmetic operation.
Now consider the given question, here the minuend value will be \[x\], here we have to determine the value of this and the subtrahend is \[ - 6\]and the value of difference is \[ - 5\].
So therefore, the given data is written as
\[x - ( - 6) = - 5\]
The minuend is unknown so we take it as x, here sign convention is applied. Therefore, the above inequality is written as
\[ \Rightarrow x + 6 = - 5\]
Now take 6 to the RHS, when transferring the number from one side to another side the sign will get changes. Therefore we have
\[ \Rightarrow x = - 5 - 6\]
On simplifying the terms which are present in the RHS the above inequality is written as
\[ \Rightarrow x = - 11\]
Therefore the value of x is -11
So, the correct answer is “x = - 11”.

Note: We can verify the obtained answer by substituting in the place of x, and we can verify it. If we get both LHS and RHS terms the same then the obtained answer is the correct one.
So now we have
\[ \Rightarrow - 11 - ( - 6) = - 5\]
Here we have to use the concept of sign conventions
\[ \Rightarrow - 11 + 6 = - 5\]
On simplifying
\[ \Rightarrow - 5 = - 5\]
Hence we have obtained LHS = RHS.