Question

How do you solve for f in $f - e + v = 2?$

Answer 1

Hint: There are three variables in the given equation, in order to solve the equation for one of the three variables, consider the other two variables to be constant and perform algebraic operations in the equation to remove the other two variables from left hand side and make the required variable a dependent variable which will depend on the values of the other two variables.

Complete step by step solution:
In order to solve the given equation for the value of f, we will first simplify the equation in such a way that all the terms in the equation (including variables and constants) except the variable f (for which we have been asked to solve the equation) should be on the right hand side of the equation and only variable f should be at the left hand side as follows
$ \Rightarrow f - e + v = 2$
Adding e to both sides of the equation, in order to remove it from left hand side,
$
\Rightarrow f - e + v + e = 2 + e \\
\Rightarrow f + v = 2 + e \\
$
Now, subtracting v from both sides, in order remove it too from the left hand side,
$
\Rightarrow f + v - v = 2 + e - v \\
\Rightarrow f = 2 + e - v \\
$
So, $f = 2 + e - v$ is the required solution for f in the equation $f - e + v = 2$

Additional information:
The given equation is similar to Euler’s polyhedron formula that is given as: $v - e + f = 2,\;where\;{\text{v,}}\;{\text{e}}\;{\text{and}}\;{\text{f}}$ are number of vertices, number of edges and the number of faces of the polyhedron respectively.

Note: In this type of question, in which equation has multiple variables, do not panic how to solve them. Just solve for the variable which you have been asked to solve for, and consider all other variables to be constant.