Question

Решение с проверкой ​

Answer 1

Пошаговое объяснение:

$\tt\displaystyle \left({x+\frac{5}{{12}}}\right)-\frac{9}{{20}}=\frac{{11}}{{15}} \hfill \\\left({x+\frac{5}{{12}}}\right)=\frac{{11}}{{15}}+\frac{9}{{20}}\hfill\\\left({x+\frac{5}{{12}}}\right)=\frac{{44}}{{60}}+\frac{{27}}{{60}}\hfill \\\left({x+\frac{5}{{12}}}\right)=\frac{{71}}{{60}} \hfill \\x=\frac{{71}}{{60}}-\frac{5}{{12}} \hfill \\x=\frac{{71}}{{60}}-\frac{{25}}{{60}}=\frac{{46}}{{60}}=\boxed{\frac{{23}}{{30}}} \hfill$

Проверка:

$\tt\displaystyle \left( {\frac{{46}}{{60}}+\frac{5}{{12}}}\right)-\frac{9}{{20}}=\frac{{46}}{{60}}+\frac{{25}}{{60}}-\frac{{27}}{{60}}=\frac{{44}}{{60}}=\frac{{11}}{{15}}$

$\[\begin{gathered}\left( {x-\frac{{11}}{{30}}} \right)-\frac{{16}}{{45}}=\frac{2}{9} \hfill \\x-\frac{{11}}{{30}}-\frac{{16}}{{45}}=\frac{2}{9} \hfill \\x=\frac{2}{9}+\frac{{16}}{{45}}+\frac{{11}}{{30}} \hfill \\x=\frac{{20}}{{90}}+\frac{{32}}{{90}}+\frac{{33}}{{30}} \hfill \\x=\frac{{85}}{{90}}=\boxed{\frac{{17}}{{18}}} \hfill \\\end{gathered} \]$

Проверка:

$\tt\displaystyle \[\left( {\frac{{85}}{{90}}-\frac{{11}}{{30}}} \right)-\frac{{16}}{{45}}=\frac{{85}}{{90}}-\frac{{33}}{{90}}-\frac{{32}}{{90}}=\frac{{20}}{{90}}=\frac{2}{9}\]$

$\[\begin{gathered}\left( {x-\frac{7}{{15}}} \right)+\frac{5}{8}=\frac{{17}}{{24}} \hfill \\x-\frac{7}{{15}}+\frac{5}{8}=\frac{{17}}{{24}} \hfill \\x=\frac{{17}}{{24}}-\frac{5}{8}+\frac{7}{{15}} \hfill \\x=\frac{{85}}{{120}}-\frac{{75}}{{120}}+\frac{{56}}{{120}} \hfill \\x=\frac{{66}}{{120}}=\boxed{\frac{{11}}{{20}}} \hfill \\ \end{gathered} \]$

Проверка:

$\tt\displaystyle \[\left( {\frac{{66}}{{120}}-\frac{7}{{15}}} \right)+\frac{5}{8}=\frac{{66}}{{120}}-\frac{{56}}{{120}}+\frac{{75}}{{120}}=\frac{{85}}{{120}}=\frac{{17}}{{24}}\]$