Step 1

we need to write all the steps according to the question.

we need to write all the operations as question says.

Step 2

x is a fraction.

x=?

According to the question, when x is multiplied by \(\displaystyle{\frac{{{10}}}{{{20}}}}\) and then added with \(\displaystyle{\frac{{{1}}}{{{15}}}}\) the result is \(\displaystyle{\frac{{{8}}}{{{6}}}}\).

\(\displaystyle\because{x}\times{\frac{{{10}}}{{{20}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}}}{{{6}}}}-{\frac{{{1}}}{{{15}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}\times{5}-{1}\times{2}}}{{{30}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{40}-{2}}}{{{30}}}}\)

\(\displaystyle\Rightarrow{x}={2}\times{\frac{{{38}}}{{{30}}}}\)

\(\displaystyle\Rightarrow{x}={\frac{{{38}}}{{{15}}}}\)

we need to write all the steps according to the question.

we need to write all the operations as question says.

Step 2

x is a fraction.

x=?

According to the question, when x is multiplied by \(\displaystyle{\frac{{{10}}}{{{20}}}}\) and then added with \(\displaystyle{\frac{{{1}}}{{{15}}}}\) the result is \(\displaystyle{\frac{{{8}}}{{{6}}}}\).

\(\displaystyle\because{x}\times{\frac{{{10}}}{{{20}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}}}{{{6}}}}-{\frac{{{1}}}{{{15}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}\times{5}-{1}\times{2}}}{{{30}}}}\)

\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{40}-{2}}}{{{30}}}}\)

\(\displaystyle\Rightarrow{x}={2}\times{\frac{{{38}}}{{{30}}}}\)

\(\displaystyle\Rightarrow{x}={\frac{{{38}}}{{{15}}}}\)