Question

How do you solve $\dfrac{t}{9}-7=-5?$

Answer 1

Hint: For these kinds of questions, we have to make use of simple and basic mathematics. We have to group all the variables together and constant together. And then make the expression as a function of the variable that we have to find out the value of. Then solve for it by doing the appropriate manipulations.

Complete step by step solution:
So we have \[\dfrac{t}{9}-7=-5\] .
The variable here is $t$ . We have to find out the value of $t$ .
So now let us transfer $-7$ from left hand side to right hand side.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow \dfrac{t}{9}-7=-5 \\
 & \Rightarrow \dfrac{t}{9}=-5+7 \\
\end{align}$
Let us add on the right hand side.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow \dfrac{t}{9}-7=-5 \\
 & \Rightarrow \dfrac{t}{9}=-5+7 \\
 & \Rightarrow \dfrac{t}{9}=2 \\
\end{align}$
Now let us cross-multiply the $9$ on the left side to the right hand side.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow \dfrac{t}{9}-7=-5 \\
 & \Rightarrow \dfrac{t}{9}=-5+7 \\
 & \Rightarrow \dfrac{t}{9}=2 \\
 & \Rightarrow t=18 \\
\end{align}$
$\therefore $ Hence, the value of $t$ in the expression $\dfrac{t}{9}-7=-5$ is $18$ .
The expression is already a function of $t$. So we do not have to shift variables to one side and constants to the other side. We certainly do not have to do any manipulations.

Note: This one is a simple question. So we can also solve this question by just substituting the value with $1,2,3...$ and figure out it’s value through a hit or trial method. But when the number of variables increases, it is really important to group all the variables of one kind together and constants to the other side to easily and quickly solve the question. Just be careful while solving to not have any calculations errors.