Question

How do you solve $3\left( 2x-3 \right)=4x$?

Answer 1

Hint: We separate the variables and the constants of the equation $3\left( 2x-3 \right)=4x$ after completing the multiplication. 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 $x$.

Complete step by step solution:
We complete the single multiplication in the equation of $3\left( 2x-3 \right)=4x$.
Multiplying 3 with $\left( 2x-3 \right)$, we get $3\left( 2x-3 \right)=6x-9$.
The equation becomes $6x-9=4x$.
The given equation $6x-9=4x$ is a linear equation of $x$. We need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $6x-9=4x$ are either variable of $x$ or a constant. We first separate the variables.
We take the variables all together to solve it.
$\begin{align}
  & 6x-9=4x \\
 & \Rightarrow 6x-4x=9 \\
\end{align}$
There is two such variables which are $6x,4x$.
Now we apply the binary operation of subtraction to get
$\Rightarrow 6x-4x=2x$.
The binary operation between them is addition which gives us $2x=9$.
Now we divide both sies of the equation with 2 to get
\[\begin{align}
  & 2x=9 \\
 & \Rightarrow \dfrac{2x}{2}=\dfrac{9}{2} \\
 & \Rightarrow x=\dfrac{9}{2} \\
\end{align}\]
Therefore, the final solution becomes \[x=\dfrac{9}{2}\].

Note: We can also solve the equation starting it with the division.
Therefore, we divide both sides of $3\left( 2x-3 \right)=4x$ by 3 and get
$\begin{align}
  & \dfrac{3\left( 2x-3 \right)}{3}=\dfrac{4x}{3} \\
 & \Rightarrow 2x-3=\dfrac{4x}{3} \\
\end{align}$
We take the variables together.
$\begin{align}
  & 2x-3=\dfrac{4x}{3} \\
 & \Rightarrow 2x-\dfrac{4x}{3}=3 \\
 & \Rightarrow \dfrac{2x}{3}=3 \\
\end{align}$ which gives \[x=\dfrac{9}{2}\]
The solution is \[x=\dfrac{9}{2}\].