\(\dfrac{1}{3}x\) + \(\dfrac{2}{5}\) ( x + 1 ) = 0
2x + \(\dfrac{1}{5}\) ( x - 5 ) = \(\dfrac{17}{5}\)
4x - ( 2x + 1 ) = 3 - \(\dfrac{1}{3}\) + x
\(\dfrac{1}{2}x\) + \(\dfrac{1}{2}\) ( x - 2 ) = \(\dfrac{3}{4}\) - 2x
3 x \(\left(x+\dfrac{1}{2}\right)\) - \(\dfrac{1}{2}\) x \(\left(4x-\dfrac{2}{3}\right)\) = \(\dfrac{5}{6}\)
a.
\(\dfrac{1}{3}x+\dfrac{2}{5}\left(x+1\right)=0\)
\(\dfrac{1}{3}x+\dfrac{2}{5}x+\dfrac{2}{5}=0\)
\(\left(\dfrac{1}{3}+\dfrac{2}{5}\right).x=-\dfrac{2}{5}\)
\(\dfrac{11}{15}x=-\dfrac{2}{5}\)
\(x=-\dfrac{2}{5}:\dfrac{11}{15}\)
\(x=-\dfrac{6}{11}\)
b.
\(2x+\dfrac{1}{5}\left(x-5\right)=\dfrac{17}{5}\)
\(2x+\dfrac{1}{5}x-1=\dfrac{17}{5}\)
\(\left(2+\dfrac{1}{5}\right).x=\dfrac{17}{5}+1\)
\(\dfrac{11}{5}x=\dfrac{22}{5}\)
\(x=\dfrac{22}{5}:\dfrac{11}{5}\)
\(x=2\)
d.
\(4x-\left(2x+1\right)=3-\dfrac{1}{3}+x\)
\(4x-2x-1=\dfrac{8}{3}+x\)
\(4x-2x-x=\dfrac{8}{3}+1\)
\(\left(4-2-1\right).x=\dfrac{11}{3}\)
\(x=\dfrac{11}{3}\)
e.
\(\dfrac{1}{2}x+\dfrac{1}{2}\left(x-2\right)=\dfrac{3}{4}-2x\)
\(\dfrac{1}{2}x+\dfrac{1}{2}x-1=\dfrac{3}{4}-2x\)
\(x-1=\dfrac{3}{4}-2x\)
\(x+2x=\dfrac{3}{4}+1\)
\(3x=\dfrac{7}{4}\)
\(x=\dfrac{7}{4}:3\)
\(x=\dfrac{7}{12}\)
f.
\(3\left(x+\dfrac{1}{2}\right)-\dfrac{1}{2}\left(4x-\dfrac{2}{3}\right)=\dfrac{5}{6}\)
\(3x+\dfrac{3}{2}-\left(2x-\dfrac{1}{3}\right)=\dfrac{5}{6}\)
\(3x+\dfrac{3}{2}-2x+\dfrac{1}{3}=\dfrac{5}{6}\)
\(3x-2x=\dfrac{5}{6}-\dfrac{3}{2}-\dfrac{1}{3}\)
\(x=-1\)
