a)\(\dfrac{1}{5}+\dfrac{4}{5}:x=0,75\)

\(\dfrac{4}{5}:x=\dfrac{11}{20}\)

\(x=\dfrac{16}{11}\)

b) \(x+\dfrac{1}{2}=1-x\)

\(2x+\dfrac{1}{2}=1\)

a)\(\dfrac{2}{5}\cdot\dfrac{5}{4}-\dfrac{3}{4}\cdot\dfrac{2}{3}\)

\(=\dfrac{1}{2}-\dfrac{1}{2}\)

\(=0\)

b)\(2\cdot\left(-\dfrac{3}{2}\right)^2-\dfrac{7}{2}\)

\(=2\cdot\dfrac{9}{4}-\dfrac{7}{2}\)

\(=\dfrac{9}{2}-\dfrac{7}{2}\)

\(=1\)

c)\(-\dfrac{3}{4}\cdot5\dfrac{3}{13}-0,75\cdot\dfrac{36}{13}\)

\(=-\dfrac{3}{4}\cdot\dfrac{68}{13}-\dfrac{3}{4}\cdot\dfrac{36}{13}\)

\(=-\dfrac{51}{13}+\dfrac{27}{13}\)

\(=-\dfrac{24}{13}\)

a)\(\sqrt{36}\cdot\left(3\sqrt{4}-\sqrt{\dfrac{1}{9}}\right)+2\)

\(=6\cdot\left(6-\dfrac{1}{3}\right)+2\)

\(=6\cdot\dfrac{17}{3}+2\)

\(=34+2\)

\(=36\)

b)\(\sqrt{\dfrac{1}{9}+\dfrac{1}{16}}\)

\(=\sqrt{\dfrac{25}{144}}\)

\(=\dfrac{5}{12}\)

c)\(\left(\sqrt{\dfrac{1}{9}}+\sqrt{\dfrac{25}{36}}-\sqrt{\dfrac{49}{81}}\right):\sqrt{\dfrac{441}{324}}\)

\(=\left(\dfrac{1}{3}+\dfrac{5}{6}-\dfrac{7}{9}\right):\sqrt{\dfrac{49}{36}}\)

\(=\dfrac{7}{18}:\dfrac{7}{6}\)

\(=\dfrac{1}{3}\)

d)\(\sqrt{\left(-\dfrac{2}{5}\right)^2}+\sqrt{1,44}-\sqrt{256}\)

\(=-\dfrac{2}{5}+1,2-16\)

\(=-0,4+1,2-16\)

\(=-15,2\)

a)\(\left(\dfrac{1}{2}+1,5\right)\cdot x=\dfrac{1}{5}\)

\(2\cdot x=\dfrac{1}{5}\)

\(x=\dfrac{1}{5}:2\)

\(x=\dfrac{1}{10}\)

b)\(\left(-1\dfrac{3}{5}+x\right):\dfrac{12}{13}=2\dfrac{1}{6}\)

\(-\dfrac{8}{5}+x=\dfrac{13}{6}\cdot\dfrac{12}{13}\)

\(-\dfrac{8}{5}+x=2\)

\(x=2+\dfrac{8}{5}\)

\(x=\dfrac{18}{5}\)

c)\(\left(x:2\dfrac{1}{3}\right)\cdot\dfrac{1}{7}=-\dfrac{3}{8}\)

\(x:\dfrac{7}{3}=-\dfrac{3}{8}\cdot7\)

\(x:\dfrac{7}{3}=-\dfrac{21}{8}\)

\(x=-\dfrac{21}{8}\cdot\dfrac{7}{3}\)

\(x=-\dfrac{49}{8}\)

d)\(-\dfrac{4}{7}\cdot x+\dfrac{7}{5}=\dfrac{1}{8}:-1\dfrac{2}{3}\)

\(-\dfrac{4}{7}\cdot x+\dfrac{7}{5}=\dfrac{1}{8}\cdot-\dfrac{3}{5}\)

\(-\dfrac{4}{7}\cdot x+\dfrac{7}{5}=-\dfrac{3}{40}\)

\(-\dfrac{4}{7}\cdot x=\dfrac{-59}{40}\)

\(x=-\dfrac{59}{40}\cdot-\dfrac{7}{4}\)

\(x=\dfrac{413}{160}\)

a)\(\dfrac{1}{2}-\left(x+\dfrac{1}{3}\right)=\dfrac{5}{6}\)

\(\dfrac{1}{2}-x-\dfrac{1}{3}=\dfrac{5}{6}\)

\(x=\dfrac{1}{2}-\left(\dfrac{5}{6}+\dfrac{1}{3}\right)\)

\(x=-\dfrac{2}{3}\)

b)\(\left(\dfrac{3}{8}-\dfrac{1}{5}\right)+\left(\dfrac{5}{8}-x\right)=\dfrac{1}{5}\)

\(\dfrac{3}{8}-\dfrac{1}{5}+\dfrac{5}{8}-x=\dfrac{1}{5}\)

\(\dfrac{4}{5}-x=\dfrac{1}{5}\)

\(x=\dfrac{3}{5}\)

a) \(-1,62+\dfrac{2}{5}+x=7\)

\(\dfrac{2}{5}+x=7+1,62\)

\(0,4+x=8,62\)

\(x=8,62-0,4\)

\(x=8,22\)

b)\(4\dfrac{3}{5}-x=-\dfrac{1}{5}+\dfrac{1}{2}\)

\(\dfrac{23}{5}-x=\dfrac{3}{10}\)

\(x=\dfrac{23}{5}-\dfrac{3}{10}\)

\(x=\dfrac{43}{10}\)

c)\(-\dfrac{4}{7}-x=\dfrac{3}{5}-2x\)

\(\Leftrightarrow-\dfrac{4}{7}-x+2x=\dfrac{3}{5}-2x+2x\)

\(\Leftrightarrow-\dfrac{4}{7}+x=\dfrac{3}{5}\)

\(x=\dfrac{3}{5}+\dfrac{4}{7}\)

\(x=\dfrac{41}{35}\)

d)\(\dfrac{5}{7}-\dfrac{1}{13}+0,25=3\dfrac{1}{2}-x\)

\(\dfrac{58}{91}+\dfrac{1}{4}=\dfrac{7}{2}-x\)

\(\dfrac{323}{364}=\dfrac{7}{2}-x\)

\(x=\dfrac{7}{2}-\dfrac{323}{364}\)

\(x=\dfrac{951}{364}\)

\(\Leftrightarrow x=\left(-0,25\right)^5:\left(-0,25\right)^3\)

\(\Leftrightarrow x=\left(-0,25\right)^2\)

\(\Leftrightarrow x=0,625\)

a) \(\dfrac{3}{4}+\dfrac{9}{5}\left(\dfrac{3}{2}-\dfrac{2}{3}\right)^2\)

\(=\dfrac{3}{4}+\dfrac{9}{5}\cdot\left(\dfrac{5}{6}\right)^2\)

\(=\dfrac{3}{4}+\dfrac{9}{5}\cdot\dfrac{25}{36}\)

\(=\dfrac{3}{4}+\dfrac{5}{4}\)

\(=\dfrac{8}{4}\)

\(=2\)

b) \(\dfrac{-22}{25}+\dfrac{22}{7}-\dfrac{3}{25}\)

\(=\dfrac{-22}{25}-\dfrac{3}{25}+\dfrac{22}{7}\)

\(=\dfrac{-25}{25}+\dfrac{22}{7}\)

\(=-1+\dfrac{22}{7}\)

\(=\dfrac{15}{7}\)