2.
\(a,\dfrac{3}{4}\cdot\left(\dfrac{1}{2}\cdot x-1\right)-\dfrac{1}{4}=-\dfrac{1}{4}\)
\(\xrightarrow[]{}\dfrac{3}{4}\cdot\left(\dfrac{1}{2}\cdot x-1\right)=-\dfrac{1}{4}+\dfrac{1}{4}\)
\(\xrightarrow[]{}\dfrac{3}{4}\cdot\left(\dfrac{1}{2}\cdot x-1\right)=0\)
\(\xrightarrow[]{}\dfrac{1}{2}\cdot x-1=0:\dfrac{3}{4}\)
\(\xrightarrow[]{}\dfrac{1}{2}\cdot x-1=0\)
\(\xrightarrow[]{}\dfrac{1}{2}\cdot x=0+1\)
\(\xrightarrow[]{}\dfrac{1}{2}\cdot x=1\)
\(\xrightarrow[]{}x=1:\dfrac{1}{2}\)
\(\xrightarrow[]{}x=2\)
\(b,1\dfrac{2}{5}-\dfrac{2}{5}\cdot\left(x+\dfrac{1}{2}\right)=\dfrac{2}{5}\)
\(\xrightarrow[]{}\dfrac{7}{5}-\dfrac{2}{5}\cdot\left(x+\dfrac{1}{2}\right)=\dfrac{2}{5}\)
\(\xrightarrow[]{}\dfrac{2}{5}\cdot\left(x+\dfrac{1}{2}\right)=\dfrac{7}{5}-\dfrac{2}{5}\)
\(\xrightarrow[]{}\dfrac{2}{5}\cdot\left(x+\dfrac{1}{2}\right)=1\)
\(\xrightarrow[]{}x+\dfrac{1}{2}=1:\dfrac{2}{5}\)
\(\xrightarrow[]{}x+\dfrac{1}{2}=\dfrac{5}{2}\)
\(\xrightarrow[]{}x=\dfrac{5}{2}-\dfrac{1}{2}\)
\(\xrightarrow[]{}x=2\)
3.
\(a)\) \(0,5+\dfrac{1}{3}+0,4+\dfrac{5}{7}+\dfrac{1}{6}-\dfrac{4}{35}\)
\(=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{5}{7}+\dfrac{1}{6}-\dfrac{4}{35}\)
\(=\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{2}{5}+\dfrac{5}{7}-\dfrac{4}{35}\right)\)
\(=1+1=2\)
\(b)\) \(\dfrac{1}{3}\cdot\dfrac{-5}{9}+\dfrac{1}{3}\cdot\dfrac{-1}{9}+4\dfrac{1}{3}\cdot\dfrac{1}{9}\)
\(=\dfrac{1}{3}\cdot\dfrac{-5}{9}+\dfrac{1}{3}\cdot\dfrac{-1}{9}+\dfrac{13}{3}\cdot\dfrac{1}{9}\)
\(=\dfrac{-5}{27}+\left[\dfrac{1}{9}\cdot\left(-\dfrac{1}{3}+\dfrac{13}{3}\right)\right]\)
\(=\dfrac{-5}{27}+\left[\dfrac{1}{9}\cdot4\right]\)
\(=\dfrac{-5}{27}+\dfrac{4}{9}=\dfrac{7}{27}\)