Question

The difference between an integer x and $\left( { - 9} \right)$ is $6$. Find all the possible values of $x$.

Answer 1

Hint: The given problem revolves around the concepts of basic arithmetic algebraic simplification. In the given question, we are required to evaluate the difference of two numbers given to us in the problem itself. One of the numbers is a variable. We break down the information given to us to try and identify what must be done in order to solve the problem. We are given the difference of two numbers. So, we form a mathematical equation for the problem and solve the equation using the transposition method to find the possible values of $x$.

Complete step by step answer:
So, we have to compute the difference between the two numbers: $x$ and $\left( { - 9} \right)$. But we are not given the order of these numbers to take the difference. We don’t know what number is to be subtracted from which number. So, we will take both the possibilities into consideration and find the values of $x$.

So, Case \[1\] : x is to be subtracted from $\left( { - 9} \right)$. So, we get,
$ \Rightarrow \left( { - 9} \right) - x$
Now, we are given the difference of the two numbers as $6$. So, we get,
$ \Rightarrow \left( { - 9} \right) - x = 6$
Now, we solve the above equation using the transposition method to find the value of x. Taking x to the right side of the equation, we get,
$ \Rightarrow \left( { - 9} \right) = 6 + x$
Now, taking all the constants to the left side of the equation to isolate the variable x, we get,
$ \Rightarrow x = - 6 - 9$
Now, simplifying the difference, we get,
$ \therefore x = - 15$
So, one possible value of x is $ - 15$.

Case $2$ : $\left( { - 9} \right)$ is to be subtracted from x.
Then, we get,
$ \Rightarrow x - \left( { - 9} \right)$
Now, we are given the difference of the two numbers as $6$. So, we get,
$ \Rightarrow x - \left( { - 9} \right) = 6$
Opening the bracket and taking all the constant terms to the right side of the equation, we get,
$ \Rightarrow x + 9 = 6$
$ \Rightarrow x = 6 - 9$
Simplifying the difference, we get,
$ \therefore x = - 3$
So, a possible value of $x$ is $ - 3$.

Hence, the possible values of x are: $ - 15$ and $ - 3$.

Note:When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of a mathematical symbol is called a mathematical expression. We must have a good grip over the mathematical operations and BODMAS rule in order to solve such questions. We must take into consideration both the cases in order to get both the values of $x$.