Question

How do you solve$3\left( y+4 \right)=4\left( y-6 \right)$?

Answer 1

Hint: The above given equation$3\left( y+4 \right)=4\left( y-6 \right)$is a linear equation in one variable. The linear equation in one variable is an equation which can be expressed in the form of $ax+b=0$, where a and b are two integers, and x is a variable and the linear equation in one variable has only one solution.

Complete step by step answer:
The given linear equation in one variable is:
$\Rightarrow 3\left( y+4 \right)=4\left( y-6 \right)$
Since, the above equation has only one variable which is y.
Now we will solve the given linear equation and find out the value of the variable y.
The equation is:
$\Rightarrow 3\left( y+4 \right)=4\left( y-6 \right)$
Now, first in the left hand side of the equation open the bracket and multiply $3$ with y and $4$. Similarly in the right hand side multiply $4$ with y and $6$, rewrite the equation as:
$\Rightarrow 3y+12=4y-24$
Now subtract $12$ from both side of the equation, then we get,
$\begin{align}
  & \Rightarrow 3y+12-12=4y-24-12 \\
 & \Rightarrow 3y=4y-36 \\
\end{align}$
Now subtract $4y$ from both side of the equation, then we get
$\begin{align}
  & \Rightarrow 3y-4y=4y-36-4y \\
 & \Rightarrow -y=-36 \\
\end{align}$
Now both negative sign get cancel out, then we get
$\Rightarrow y=36$

Hence we get the value of the variable y which is $36$.

Note: We can also check if our value of variable y is correct or not. For the put the value of y in the given equation which is:
$\Rightarrow 3\left( y+4 \right)=4\left( y-6 \right)$
Now putting $y=36$ in the above equation, then we get
$\begin{align}
  & \Rightarrow 3\left( 36+4 \right)=4\left( 36-6 \right) \\
 & \Rightarrow 3\left( 40 \right)=4\left( 30 \right) \\
\end{align}$
Now if we multiply the $3$ with $40$ and similarly multiply $4$ with $30$, then we get
$\Rightarrow 120=120$
Thus, our left and right side of the above equation becomes equal. It means the value of the variable y is correct.