Question

How do you solve $6y-20=2y-4$?

Answer 1

Hint: We separate the variables and the constants of the equation $6y-20=2y-4$. We apply the binary operation of addition and subtraction for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer to equate with 0. Then we solve the linear equation to find the value of $y$.

Complete step-by-step solution:
The given equation $6y-20=2y-4$ is a linear equation of $y $. We need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $6y-20=2y-4$ are either variable of $y$ or a constant. We first separate the variables and the constants to solve it.
$\begin{align}
  & 6y-20=2y-4 \\
 & \Rightarrow 6y-2y=20-4 \\
\end{align}$
There are two such variables which are $6y$ and $2y$.
Now we apply the binary operation of subtraction to get
$\Rightarrow 6y-2y=4y$
There are two such constants which are 20 and 4.
Now we apply the binary operation of subtraction to get
$\Rightarrow 20-4=16$
The final equation gives us $4y=16$.
Now we divide both sides of the equation with 4 to get
\[\begin{align}
  & 4y=16 \\
 & \Rightarrow \dfrac{4y}{4}=\dfrac{16}{4} \\
 & \Rightarrow y=4 \\
\end{align}\]
Therefore, the final solution becomes \[y=4\].

Note: We can verify the result of the equation $6y-20=2y-4$ by taking the value of as \[y=4\].
Therefore, the left-hand side of the equation $6y-20=2y-4$ becomes
$6y-20=6\times 4-20=24-20=4$.
The right-hand side of the equation $6y-20=2y-4$ becomes
$2y-4=2\times 4-4=8-4=4$.
Thus, verified for the equation $6y-20=2y-4$ the solution is \[y=4\].