Question

If $3x+5=6-7x$, then x=?

Answer 1

Hint: We here have to solve the equation given as $3x+5=6-7x$. We will solve this by first separating the terms containing x and the constant terms on different sides of the equal sign, i.e. one of them on the RHS and the other on the LHS. Then we will simplify both the sides. Then we will make the coefficient of x as one. Then we will get the final value of x which will be our required answer.

Complete step by step answer:
We here have been given the equation in x as $3x+5=6-7x$. To find the value of x, we will need to solve it.
It is solved as follows:
The given equation is:
$3x+5=6-7x$
Now, we will bring the terms in ‘x’ on the same side. This is done as follows:
$\begin{align}
  & 3x+5=6-7x \\
 & \Rightarrow 3x+7x+5=6 \\
\end{align}$
Now, we will take the constants to the other separate side of the equation. This is done as follows:
$\begin{align}
  & 3x+7x+5=6 \\
 & \Rightarrow 3x+7x=6-5 \\
\end{align}$
Now, we will simplify both the RHS and the LHS. This is done as follows:
$\begin{align}
  & 3x+7x=6-5 \\
 & \Rightarrow 10x=1 \\
\end{align}$
Now, we can see that the coefficient of x is not 1. We will thus try to make it 1. This is done as follows:
The equation has now become:
$10x=1$
We can see that the coefficient of x is 10. Thus, we will divide both the RHS and the LHS by 10 to make the coefficient of x as 1. This is done as follows:
$\begin{align}
  & 10x=1 \\
 & \Rightarrow \dfrac{10x}{10}=\dfrac{1}{10} \\
 & \therefore x=\dfrac{1}{10} \\
\end{align}$

Thus, the value of x is $\dfrac{1}{10}$.

Note: We here have explained each and every step in this question but we need not to do it this way. We can club two or three steps together and do it a little faster. It is done as follows:
$\begin{align}
  & 3x+5=6-7x \\
 & \Rightarrow 3x+7x=6-5 \\
 & \Rightarrow 10x=1 \\
 & \therefore x=\dfrac{1}{10} \\
\end{align}$
After getting the value of x it is advised to verify the answer by re-substituting it in the given equation and check if both RHS and LHS are the same. This is a simple calculation, so students must be very careful not to make mistakes in sign while taking similar terms on one side.