Question

[1,(3) •X +0,2]: 0,375 = 2,(6)​

Answer 1

$\it 1,(3)=1\dfrac{3}{9}=\dfrac{\ 12^{(3}}{9} = \dfrac{4}{3}\\ \\ \\ 0,2=\dfrac{\ \ 2^{(2}}{10}=\dfrac{1}{5}\\ \\ \\ 0,375=\dfrac{\ \ 375^{(25}}{1000}=\dfrac{\ \ 15^{(5}}{40}=\dfrac{3}{8}\\ \\ \\ 2,(6)=2\dfrac{6}{9}=\dfrac{\ \ 24^{(3}}{9}=\dfrac{8}{3}$

Ecuația  devine :

$\it \Big(\dfrac{4}{3}x+\dfrac{1}{5}\Big) :\dfrac{3}{8}=\dfrac{8}{3} \Rightarrow \dfrac{4}{3}x+\dfrac{1}{5}=\dfrac{8}{3}\cdot\dfrac{3}{8} \Rightarrow \dfrac{4}{3}x+\dfrac{1}{5}=1 \Rightarrow\\ \\ \\ \Rightarrow \dfrac{4}{3}x=1-\dfrac{1}{5} \Rightarrow \dfrac{4}{3}x=\dfrac{4}{5} \Rightarrow x=\dfrac{4}{5}\cdot\dfrac{3}{4} \Rightarrow x=\dfrac{3}{5}=0,6$