Question

How do you solve the equation $6x=4x-\left( -18 \right)$?

Answer 1

Hint: We separate the variables and the constants of the equation $6x=4x-\left( -18 \right)$. We have in total one multiplication. We multiply the constant. Then we apply the binary operation of subtraction for variables. 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 x.

Complete step-by-step solution:
The given equation $6x=4x-\left( -18 \right)$ is a linear equation of x. We need to simplify the equation by completing the multiplication of the constants separately.
All the terms in the equation of $6x=4x-\left( -18 \right)$ are either variable of x or a constant. We break the multiplication by multiplying $-1$ with $\left( -18 \right)$. So, $-\left( -18 \right)=18$.
The equation becomes
$\begin{align}
  & 6x=4x-\left( -18 \right) \\
 & \Rightarrow 6x=4x+18 \\
\end{align}$.
We take the variables and the constants on opposite sides and get $6x-4x=18$.
There are two variables which are $6x$ and $4x$.
The binary operation between them is subtraction which gives us $6x-4x=2x$.
Now we take the constants. There is only one constant which is 18.
The final solution becomes
$\begin{align}
  & 6x=4x+18 \\
 & \Rightarrow 2x=18 \\
\end{align}$.
Now we divide both sides with 2 and get
\[\begin{align}
  & \dfrac{2x}{2}=\dfrac{18}{2} \\
 & \Rightarrow x=9 \\
\end{align}\]
Therefore, the solution is $x=9$.

Note: We can verify the result of the equation $6x=4x-\left( -18 \right)$ by taking the value of x as $x=9$.
Therefore, the left-hand side of the equation becomes \[6x=6\times 9=54\].
The right-hand side of the equation becomes \[4x-\left( -18 \right)=4\times 9+18=36+18=54\].
Thus, verified for the equation $6x=4x-\left( -18 \right)$, the solution is $x=9$.