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# How do you solve the $\dfrac{7}{y} - \dfrac{7}{4} = \dfrac{1}{4}$?

Last updated date: 13th Jun 2024
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Hint: In the given problem we need to solve this for ‘y’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘y’ terms one side and constants on the other side of the equation.

Complete step-by-step solution:
Given, $\dfrac{7}{y} - \dfrac{7}{4} = \dfrac{1}{4}$.
Now we consider $- \dfrac{7}{4}$ as one term.
We transpose $- \dfrac{7}{4}$ which is present in the left hand side of the equation to right hand side said of the equation by adding $\dfrac{7}{4}$ on the right hand side of the equation.
$\dfrac{7}{y} = \dfrac{1}{4} + \dfrac{7}{4}$
Taking LCM and solving we have,
$\dfrac{7}{y} = \dfrac{{1 + 7}}{4}$
$\dfrac{7}{y} = \dfrac{8}{4}$
$\dfrac{7}{y} = \dfrac{2}{1}$
Taking reciprocal of above equation we have,
$\dfrac{y}{7} = \dfrac{1}{2}$
Transpose 7 to the right hand side of the equation by multiplying 7 on the right hand side of the equation,
$y = \dfrac{1}{2} \times 7$
$\Rightarrow y = \dfrac{7}{2}$
In decimal form we have,
$\Rightarrow y = 3.5$
$\dfrac{7}{{\left( {\dfrac{7}{2}} \right)}} - \dfrac{7}{4} = \dfrac{1}{4}$
$\dfrac{{2 \times 7}}{7} - \dfrac{7}{4} = \dfrac{1}{4}$
$2 - \dfrac{7}{4} = \dfrac{1}{4}$
$\dfrac{{8 - 7}}{4} = \dfrac{1}{4}$
$\Rightarrow \dfrac{1}{4} = \dfrac{1}{4}$