a) \(\dfrac{3}{7}+\dfrac{1}{7}:x=\dfrac{3}{14}\)
\(\Rightarrow\dfrac{1}{7}:x=\dfrac{3}{14}-\dfrac{3}{7}\)
\(\Rightarrow\dfrac{1}{7}:x=-\dfrac{3}{14}\)
\(\Rightarrow x=\dfrac{1}{7}:-\dfrac{3}{14}\)
\(\Rightarrow x=-\dfrac{2}{3}\)
b) \(\dfrac{11}{3}+\dfrac{26}{7}x=\dfrac{3}{2}\)
\(\Rightarrow\dfrac{26}{7}x=\dfrac{3}{2}-\dfrac{11}{3}\)
\(\Rightarrow\dfrac{26}{7}x=-\dfrac{13}{6}\)
\(\Rightarrow x=-\dfrac{13}{6}:\dfrac{26}{7}\)
\(\Rightarrow x=-\dfrac{7}{12}\)
c) \(x+3,5-\dfrac{4}{7}=\dfrac{1}{2}-4\dfrac{1}{8}\)
\(\Rightarrow x+\dfrac{7}{2}-\dfrac{4}{7}=\dfrac{1}{2}-\dfrac{33}{8}\)
\(\Rightarrow x+\dfrac{41}{14}=-\dfrac{29}{8}\)
\(\Rightarrow x=-\dfrac{29}{8}-\dfrac{41}{14}\)
\(\Rightarrow x=-\dfrac{367}{56}\)
d) \(7,2x+\left(-3,7x\right)-2,7=7,8\)
\(\Rightarrow7,2x-3,7x-2,7=7,8\)
\(\Rightarrow3,5x=7,8+2,7\)
\(\Rightarrow3,5x=10,5\)
\(\Rightarrow x=\dfrac{10,5}{3,5}\)
\(\Rightarrow x=3\)
e) \(3\left(x-\dfrac{1}{2}\right)=-x+\dfrac{1}{5}\)
\(\Rightarrow3x-\dfrac{3}{2}=-x+\dfrac{1}{5}\)
\(\Rightarrow3x+x=\dfrac{1}{5}+\dfrac{3}{2}\)
\(\Rightarrow4x=\dfrac{17}{10}\)
\(\Rightarrow x=\dfrac{17}{10}:4\)
\(\Rightarrow x=\dfrac{17}{40}\)
f) \(\left(\dfrac{1}{4}-x\right)\left(x+\dfrac{2}{5}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{1}{4}-x=0\\x+\dfrac{2}{5}=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=-\dfrac{2}{5}\end{matrix}\right.\)
g) \(\left(2x-3\right)^2=36\)
\(\Rightarrow\left(2x-3\right)^2=6^2\)
\(\Rightarrow\left[{}\begin{matrix}2x-3=6\\2x-3=-6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=9\\2x=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
h) \(7^{x+2}+2\cdot7^x=357\)
\(\Rightarrow7^x\cdot\left(7^2+2\right)=357\)
\(\Rightarrow7^x\cdot\left(49+2\right)=357\)
\(\Rightarrow7^x\cdot51=357\)
\(\Rightarrow7^x=\dfrac{357}{51}\)
\(\Rightarrow7^x=7^1\)
\(\Rightarrow x=1\)
