Question

How do you simplify $7x+7y=7(x+?)$ ?

Answer 1

Hint: In this question we will check for the factor which is common to both the terms in the left-hand and the right-hand side and divide the factor to find the missing element which is denoted by $?$ in the question.

Complete step by step answer:
We have the expression as $7x+7y=7(x+?)$
Now on both the sides we can see that $7$ is a factor for all the elements on the left-hand side and the right-hand side of the expression, we will divide both the sides of the expression by $7$.
On dividing, we get:
$\Rightarrow \dfrac{7x+7y}{7}=\dfrac{7(x+?)}{7}$
Now on splitting the denominator in the left-hand side of the expression, we get:
$\Rightarrow \dfrac{7x}{7}+\dfrac{7y}{7}=\dfrac{7(x+?)}{7}$
Now on simplifying the terms, we get:
$\Rightarrow x+y=x+?$
Now on transferring the term $x$ from the left-hand side of the expression to the right-hand side of the expression, we get:
$\Rightarrow y=x-x+?$
On simplifying the expression, we get:
$\Rightarrow y=?$ , which indicates that the value of the unknown variable $?$ is $y$, which is the required solution.

Note: It is to be remembered that the question can be done by simplifying the left-hand side of the expression by taking the common from it and then comparing it with the right-hand side. It can be done as:
Consider the left-hand side of the equation:
$\Rightarrow 7x+7y$
Now the term $7$is common in both the terms therefore, on taking it out as common, we get:
$\Rightarrow 7(x+y)$
Now on comparing it with the right-hand side, we can write the expression as:
$\Rightarrow 7(x+y)=7(x+?)$
On comparing we can see that $y=?$, which is the same solution as we have got above.
It is to be remembered that whenever a number which is in addition or subtraction is transferred across the $=$ sign, the number converts into subtraction and addition respectively.