Question

What is the value of $'x'$ in the equation: $3\left( x-4 \right)=2x-\left( 3x-4 \right)$?

Answer 1

Hint: We solve this problem by using the standard property that is distributive property. The distributive property is given as,
$a\left( b+c \right)=ab+ac$
Then we take all the variables to one side and the constant to the other side so that we can calculate the required value of the variable. Then we check the result we got by substituting the value of $'x'$ in the given equation or confirmation.

Complete step by step solution:
We are asked to find the value of variable in the equation given as,
$3\left( x-4 \right)=2x-\left( 3x-4 \right)$
Now, let us use the distributive property of the numbers.
We know that the distributive property of the numbers is given as,
$a\left( b+c \right)=ab+ac$
Here, we can see that this property can be used in both LHS and RHS of the given equation.
By using the above distributive property to the given equation then we get,
$\begin{align}
  & \Rightarrow 3x-12=2x-3x+4 \\
 & \Rightarrow 3x-12=-x+4 \\
\end{align}$
Now, let us take all the variables to one side and the constants to other sides then we get,
$\begin{align}
  & \Rightarrow 3x+x=12+4 \\
 & \Rightarrow 4x=16 \\
\end{align}$
Now, let us divide both sides of the equation with 4 then we get,
$\begin{align}
  & \Rightarrow \dfrac{4x}{4}=\dfrac{16}{4} \\
 & \Rightarrow x=4 \\
\end{align}$
Therefore, we can conclude that the value of the variable in the given equation $3\left( x-4 \right)=2x-\left( 3x-4 \right)$ is given as,
$\therefore x=4$
Now, let us verify the result that we got is correct or wrong.
Let us substitute $x=4$ in LHS of the given equation then we get,
$\begin{align}
  & \Rightarrow LHS=3\left( 4-4 \right) \\
 & \Rightarrow LHS=0 \\
\end{align}$
Now, let us substitute $x=4$ in RHS of the given equation then we get,
$\begin{align}
  & \Rightarrow RHS=2\left( 4 \right)-\left( 3\left( 4 \right)-4 \right) \\
 & \Rightarrow RHS=8-\left( 12-4 \right) \\
 & \Rightarrow RHS=8-8=0 \\
\end{align}$
Here, we can see that both LHS and RHS are equal.
Therefore we can say that the result we got that is $x=4$ is the correct answer.

Note: We need to check if the result that we got is correct or wrong by substituting the result in the given equation. We might sometimes make some calculation mistakes or in some cases we might get the result that is not in the domain of the given function.
So, after solving these types of problems we need to check the result and get confirmation.