Question

Solve the following relation and check the result: 4z + 3 = 6 + 2z

Answer 1

Hint: First we take all the terms containing z to one side and all the constant terms to the other side and then we will use some algebraic operation like subtraction and multiplication. After that we will put the value of z then we have got in 4z + 3 = 6 + 2z to check if the result that we have got is correct or not.

Complete step-by-step answer:
Let’s start solving the question.
We have been given 4z + 3 = 6 + 2z
Now taking 2z and 3 to the opposite sides we get,
$\begin{align}
  & 4z-2z=6-3 \\
 & 2z=3 \\
 & z=\dfrac{3}{2} \\
\end{align}$
Hence, we have found the value of z which comes out to be $\dfrac{3}{2}$.
Now we do the checking part.
So, to check the result that we have got is true or not we will put the value of $z=\dfrac{3}{2}$ in
4z + 3 = 6 + 2z and find the value of LHS and RHS separately.
Let’s first check LHS,
Putting the value of $z=\dfrac{3}{2}$ in LHS we get,
$\begin{align}
  & =4\left( \dfrac{3}{2} \right)+3 \\
 & =6+3 \\
 & =9 \\
\end{align}$
Now we put the value of $z=\dfrac{3}{2}$ in RHS,
$\begin{align}
  & =6+2\left( \dfrac{3}{2} \right) \\
 & =6+3 \\
 & =9 \\
\end{align}$
Hence we can see that LHS = RHS.
So, the value of $z=\dfrac{3}{2}$ is correct.

Note: One can solve this question by using some other algebraic operation in some of the steps but in the end the answer that we will get will be the same. So, there is no fixed rule that we need no subtract first, we can use any operation we like to solve this question.