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# Find the value of y:$\dfrac{3y-2}{7}-\dfrac{5y-8}{4}=\dfrac{1}{14}$

Last updated date: 22nd Jul 2024
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Hint: For the type of question we need to find out the value of the variable in the equation we have. Here in our case it is ‘y’. We can find out by simplifying the equation, where we will get the linear form of equation in terms of y. Where we can easily find out the value of y through the method of linear equation in one variable.

$\dfrac{3y-2}{7}-\dfrac{5y-8}{4}=\dfrac{1}{14}$
\begin{align} & \dfrac{4\left( 3y-2 \right)}{28}-\dfrac{7\left( 5y-8 \right)}{28}=\dfrac{1}{14} \\ & \dfrac{12y-8}{28}-\dfrac{35y-56}{28}=\dfrac{1}{14} \\ & \dfrac{12y-8-35y+56}{28}=\dfrac{1}{14} \\ & \dfrac{-23y+48}{28}=\dfrac{1}{14} \\ \end{align}
$\dfrac{-23y+48}{2}=\dfrac{1}{1}$
\begin{align} & -23y+48=2 \\ & 48-2=23y \\ & 46=23y \\ & y=\dfrac{46}{23} \\ & y=2 \\ \end{align}