Question

How do you solve for “c” in $ 3abc + b = 5?$

Answer 1

Hint: First simplify the given equation with help of algebraic operations, in such a way that the terms not having “c” in it, should be at the right hand side of the equation and only the term having “c” in it should be on the left hand side. Then divide both sides of the equation with a coefficient of “c”, in order to get the required solution.

Complete step by step solution:
 In order to solve the given equation $3abc + b = 5$ for the variable “c”, we will assume all other variables except “c” to be constant and then simplify the equation with help of algebraic operation, such that term consisting “c” will be on the left hand side and rest other terms on the right hand side. See the following way to know how we will do it,
\[ \Rightarrow 3abc + b = 5\]
Subtracting “b” from both sides, in order to remove it from left hand side, we will get
$
   \Rightarrow 3abc + b - b = 5 - b \\
   \Rightarrow 3abc = 5 - b \\
 $
Now, dividing both sides with coefficient of “c”, in order to get the required solution,
In the term $3abc$, coefficient of “c” will be equal to $3ab$
Dividing both sides of the above equation with $3ab$, we will get
$
   \Rightarrow \dfrac{{3abc}}{{3ab}} = \dfrac{{5 - b}}{{3ab}} \\
   \Rightarrow c = \dfrac{{5 - b}}{{3ab}} \\
 $
Therefore $c = \dfrac{{5 - b}}{{3ab}}$ is the required solution for “c” in the equation $3abc + b = 5$

Note: Coefficient of a variable in any term that consist of more variables (like in this question) and also constant, coefficient of that particular variable is equal to the term left after removal of the variable (whose coefficient is wanted) from it.