Question

How do you solve $2+6v=-8-4v$?

Answer 1

Hint: We have a linear equation of $v$. There are two variable terms and two constants. We take all the variables and the constants in one side of the equality. Then we perform the binary operations between them. We solve the final equation to find the value of $v$.

Complete step by step solution:
The given equation $2+6v=-8-4v$ is a linear equation of $v$. we need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $2+6v+8+4v=0$ are either variable of $v$ or a constant. We first separate the variables and the constants.
We take the variables to get $6v+4v$.
The binary operation of addition gives $6v+4v=10v$.
We take the constants all together to solve it.
There are two such constants which are 2 and 8.
Now we apply the binary operation of addition to get $2+8=10$.
The binary operation of addition gives us $10v+10=0$ which gives $10v=-10$.
Now we divide both sides of the equation with 10 to get
\[\begin{align}
  & 10v=-10 \\
 & \Rightarrow \dfrac{10v}{10}=\dfrac{-10}{10} \\
 & \Rightarrow v=-1 \\
\end{align}\]
Therefore, the final solution becomes \[v=-1\].
We can also solve the equation starting it with the division.

Note: We can verify the result of the equation $2+6v=-8-4v$ by taking the value of as \[v=-1\].
Therefore, the left-hand side of the equation becomes $2+6v=2+6\times \left( -1 \right)=-4$.
The right-hand side of the equation becomes $-8-4v=-8-4\times \left( -1 \right)=-4$.
Thus, verified for the equation $2+6v=-8-4v$ the solution is \[v=-1\].
We can also divide both sides of $2+6v=-8-4v$ by 2 and get
\[\begin{align}
  & \dfrac{2+6v}{2}=\dfrac{-8-4v}{2} \\
 & \Rightarrow \dfrac{2}{2}+\dfrac{6v}{2}=\dfrac{-8}{2}-\dfrac{4v}{2} \\
\end{align}\]
We take the constants fractions together.
$\begin{align}
  & \dfrac{2}{2}+\dfrac{6v}{2}=\dfrac{-8}{2}-\dfrac{4v}{2} \\
 & \Rightarrow 1+3v=-4-2v \\
\end{align}$
We separate the variables and the constants to get
\[\begin{align}
  & \Rightarrow 3v+2v=-1-4 \\
 & \Rightarrow 5v=-5 \\
 & \Rightarrow v=-1 \\
\end{align}\]
The solution is \[v=-1\].