Question

How do you solve for b in $2a + 2b = c?$

Answer 1

Hint: The given equation is consist of three variables, to solve it for b, first simplify the it with the help of algebraic operations, in such a manner that the terms (including variables and constants) except the one containing b, should be at right hand side of the equation and the only term having b in it should be on the left hand side. After simplifying, divide both sides of the equation with coefficient of c, to get the required solution.

Complete step by step solution:
In order to solve the given equation $2a + 2b = c$, for the variable b, we need to simplify it first as follows
$ \Rightarrow 2a + 2b = c$
We will first send all variables and constants except the term with b in it, present in the equation to right hand side of the equation with help of algebraic operations
Subtracting both sides of the above equation with $2a$, to send it to the right hand side, we will get
$
\Rightarrow 2a + 2b - 2a = c - 2a \\
\Rightarrow 2b = c - 2a \\
$
Now we have only term with b present on the left hand side,
Dividing both sides with coefficient of b to get the required solution for b
$
\Rightarrow \dfrac{{2b}}{2} = \dfrac{{c - 2a}}{2} \\
\Rightarrow b = \dfrac{{c - 2a}}{2} \\
$
Therefore $b = \dfrac{{c - 2a}}{2}$ is the required solution for b in the equation $2a + 2b = c$

Note: In this type of questions, where the number of variables is more than the number of equations (as in this case three variables and only one equation), solutions for a variable will always come in terms of the other variables of the equation, as we get in this question. For a particular numerical solution, the number of variables and number of equations have to be equal.