Question

How do you solve \[4\left( 3-y \right)=6-2\left( 1-3y \right)\]?

Answer 1

Hint: In this problem, we have to solve the given expression and find the value of y. We can first multiply the numbers (which are outside) inside the brackets in the both left-hand side and the right-hand side. We can then simplify the numbers by taking the terms with y to one side and the remaining terms to the other side then we can simplify to find the value of y.

Complete step by step solution:
We know that the given equation to be solved is,
\[4\left( 3-y \right)=6-2\left( 1-3y \right)\]
We can now multiply the numbers inside the bracket in the both left-hand side and the right-hand side of the equation, we get
\[\Rightarrow 12-4y=6-2+6y\]
We can now simplify the above step, we get
\[\Rightarrow 12-4y=4+6y\] ….. (1)
We can now take the terms with y to the left-hand side and the remaining terms to the right-hand side by changing the sign respectively, we get
\[\Rightarrow -6y-4y=4-12\]
We can now simplify the above step in the both left-hand side and the right-hand side of the equation. we get
\[\Rightarrow -10y=-8\]
We can now divide -10 on both the side of the above step, we get
\[\Rightarrow y=\dfrac{8}{10}=\dfrac{4}{5}\]
Therefore, the value of \[y=\dfrac{4}{5}\].

Note: Students make mistakes while separating the terms with variables on one side and the other terms to the other side, by changing the sign respectively. We can now check for the answer to be correct by substituting it in the given equation.
We can now substitute \[y=\dfrac{4}{5}\] in (1), we get
\[\begin{align}
  & \Rightarrow 12-4\left( \dfrac{4}{5} \right)=4+6\left( \dfrac{4}{5} \right) \\
 & \Rightarrow 12-\dfrac{16}{5}=4+\dfrac{24}{5} \\
 & \Rightarrow 8.8=8.8 \\
\end{align}\]
Therefore, the answer is correct.