Question

How do you solve for $k$ in $3k+6t=b+5$ ?

Answer 1

Hint: For these kinds of questions ,all we need to be aware of is simple and basic mathematics. We need to group constants to one side and variables to the other. If there are more than one kind of variable, then we need to group all the variables of one kind together and variables of other kinds together. After doing so, we need to manipulate the equation if necessary so as to simplify. After doing so, we just need to use some basic operations such as additions or subtractions according to the question and find out the answer.

Complete step by step solution:
Here we can clearly see that we have three variables namely $k,t,b$ . But we are not given three equations involving these three variables to solve for the absolute value of them.
Since we have only one equation with three unknown variables, we can only write one variable in the terms of the other two variables. It would just be a mere relation between the three.
Now let us send all the unrequired variables onto the right side of the equation.
Let us $6t$ from the left hand side to the right hand side of the equation.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 3k+6t=b+5 \\
 & \Rightarrow 3k=b+5-6t \\
\end{align}$
Now let us divide the entire equation with $3$.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 3k+6t=b+5 \\
 & \Rightarrow 3k=b+5-6t \\
 & \Rightarrow k=\dfrac{b}{3}+\dfrac{5}{3}-2t \\
\end{align}$
$\therefore $ Upon solving $3k+6t=b+5$, we get $k=\dfrac{b}{3}+\dfrac{5}{3}-2t$.

Note: We have to be careful while solving these kinds of questions. We should also be careful with the signs of each number as the sign of a number changes as it transfers from one side of the equation to the other side of the question. This is only a relation between $k,t,b$. We can’t really find the absolute values of any of the three unknown variables present in this question as we have insufficient equations. If there are any manipulations that are to be done before solving, they should be done quickly and accurately.