Question

How do you solve \[\dfrac{{3n}}{5} - \dfrac{2}{5} = \dfrac{7}{{10}}\]?

Answer 1

Hint: In the given problem we need to solve this for ‘n’. 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 ‘n’ terms one side and constants on the other side of the equation.

Complete step by step answer:
Given \[\dfrac{{3n}}{5} - \dfrac{2}{5} = \dfrac{7}{{10}}\].
We transpose \[ - \dfrac{2}{5}\] which is in the left side of the equation to right hand side of the equation by adding \[\dfrac{2}{5}\]to the right hand side of the equation.
\[\dfrac{{3n}}{5} = \dfrac{7}{{10}} + \dfrac{2}{5}\]
Taking LCM and simplifying we have,
\[\dfrac{{3n}}{5} = \dfrac{{7 + 4}}{{10}}\]
\[\dfrac{{3n}}{5} = \dfrac{{11}}{{10}}\]
We transpose 5 to the right hand side of the equation by multiplying 5 to the right hand side of the equation.
\[3n = \dfrac{{11}}{{10}} \times 5\]
\[3n = \dfrac{{11}}{2}\]
We transpose 3 to the right hand side of the equation by dividing 3 to the right hand side of the equation.
\[n = \dfrac{{11}}{{2 \times 3}}\]
\[ \Rightarrow n = \dfrac{{11}}{6}\]. This is the required answer.

Note: We can check whether the given solution is correct or wrong. To check we need to substitute value of ‘n’ in the given problem we have
\[\dfrac{{3\left( {\dfrac{{11}}{6}} \right)}}{5} - \dfrac{2}{5} = \dfrac{7}{{10}}\]
\[\dfrac{{\left( {\dfrac{{11}}{2}} \right)}}{5} - \dfrac{2}{5} = \dfrac{7}{{10}}\]
\[\dfrac{{11}}{{5 \times 2}} - \dfrac{2}{5} = \dfrac{7}{{10}}\]
\[\dfrac{{11}}{{10}} - \dfrac{2}{5} = \dfrac{7}{{10}}\]
\[\dfrac{{11 - 4}}{{10}} = \dfrac{7}{{10}}\]
\[ \Rightarrow \dfrac{7}{{10}} = \dfrac{7}{{10}}\].
Hence the given answer is correct.
If we want to transpose the addition number to any side of the equation we subtract it with the same number on both sides of the equation. Similarly if we want to transpose the negative number to any side of the equation we add with the same number on both sides of the equation. Similarly if we have multiplication we use division to transpose. If we have division we use multiplication to transpose. Follow the same procedure for these kinds of problems.