Question

Solve that $\dfrac{y-4}{3}+3y=4$

Answer 1

Hint: In the question we are given an equation which is a linear equation in one variable. To understand this we will first learn definitions and examples of variables, constants, degree of an equation, linear equation. Then we will learn the transposition method and we will use this method to solve our given equation.

Complete step by step answer:
In the question we are given a linear equation in one variable.
Variable:
 Variable is a symbol whose value is not fixed means its value can vary. We usually denotes variable with alphabets like $x,y,z$ and so on
Constant:
Constant is a value whose value is fixed means we cannot change its value
Example: $1,2,5,77,100$
Equation:
An Equation is a mathematical statement which consists of variables and constants.
An equation can consist of more than one variable.
Example:
$x+5y=48$ $......eq\left( 1 \right)$
$4y=85$ $......eq\left( 2 \right)$
${{a}^{2}}=81$ $......eq\left( 3 \right)$
In $eq\left( 1 \right)$ we have two variables $x\And y$ and $48$ is constant, in $eq\left( 2 \right)$ we have only one variable$y$ and $45$ is constant and in $eq\left( 3 \right)$ we have only one variable $a$ and $81$ is constant.
Degree of an equation:
Degree of an equation is the highest power of the variable in the equation.
Example:
${{x}^{8}}+{{x}^{4}}+55=88$
In this the variable is $x$ and highest power of $x$ is $8$ , so degree of our given equation is $8$
Linear equation:
Linear equation is an equation whose degree is $1$ or we can say that whose highest power of variable is $1$ .
Example:
$\begin{align}
  & a+b+c=8......eq\left( 1 \right) \\
 & y+5=7......eq\left( 2 \right) \\
\end{align}$
These both are linear equations where $eq\left( 1 \right)$ is in three variables $a,b\And c$ and $eq\left( 2 \right)$ is in one variable $y$ .
Linear equation in one variable:
Linear equation is an equation whose degree is $1$ and consists of one variable only.
Example:
$\begin{align}
  & x+5=8 \\
 & z+7=52 \\
\end{align}$
These two equations are linear equations in one variable
Basic method to solve linear equation in one variable is Transposition
In transposition method
We shift or transpose various operations from right hand side to left hand side or from left hand side to right hand side.
$+$ Will transpose into $-$
$-$ Will transpose into $+$
$\times $ Will transpose into $\div $
$\div $ Will transpose into $\times $
Now we have learned basic terminology which is required for this question.
Now we will proceed to our question.
In the question we have to solve our given equation,
Our given equation is $\dfrac{y-4}{3}+3y=4$
We will first try to simplify the left hand side.
$\dfrac{y-4+9y}{3}=4$
Now we will transpose $3$ to right hand side
$y-4+9y=12$
We will transpose $-4$ to right hand side
$y+9y=12+4$
Now we will simplify left hand side and right hand side
$10y=16$
We will transpose $10$ to right hand side
$\begin{align}
  & y=\dfrac{16}{10} \\
 & \Rightarrow y=\dfrac{8}{5} \\
\end{align}$
$\therefore y=\dfrac{8}{5}$ is our required answer.

Note:
Linear equations can be of two or three or more variables. To solve linear equations of two variables we have four methods named as graphical method, substitution method, elimination method, cross multiplication method. To solve linear equations in two variables we need at least two equations of the same variable.