Решите уравнение: 1) 2х/7=3+x/8 2) 7x/5=2+x/9 3) 2-x/7=3+x/14 4) 7-x/5=2+x/15 5) x/14+x/16=5 6) x/15+x/27=3 7) x/3+x+1/7=x-2/6 8) x/2+x-1/4=x+2/9

Решу по шагам.

1. $\dfrac{2x}{7}=3+\dfrac{x}{8}$
   $\dfrac{2x}{7}-\dfrac{x}{8}=3\Rightarrow \dfrac{16x-7x}{56}=3\Rightarrow \dfrac{9x}{56}=3\Rightarrow x=\dfrac{56}{3}$.

2. $\dfrac{7x}{5}=2+\dfrac{x}{9}$
   $\dfrac{7x}{5}-\dfrac{x}{9}=2\Rightarrow \dfrac{63x-5x}{45}=2\Rightarrow \dfrac{58x}{45}=2\Rightarrow x=\dfrac{45}{29}$.

3. $2-\dfrac{x}{7}=3+\dfrac{x}{14}$
   $-\dfrac{x}{7}-\dfrac{x}{14}=1\Rightarrow \dfrac{-2x-x}{14}=1\Rightarrow -\dfrac{3x}{14}=1\Rightarrow x=-\dfrac{14}{3}$.

4. $7-\dfrac{x}{5}=2+\dfrac{x}{15}$
   $-\dfrac{x}{5}-\dfrac{x}{15}=-5\Rightarrow \dfrac{-3x-x}{15}=-5\Rightarrow -\dfrac{4x}{15}=-5\Rightarrow x=\dfrac{75}{4}$.

5. $\dfrac{x}{14}+\dfrac{x}{16}=5$
   $\dfrac{8x+7x}{112}=5\Rightarrow \dfrac{15x}{112}=5\Rightarrow x=\dfrac{112}{3}$.

6. $\dfrac{x}{15}+\dfrac{x}{27}=3$
   $\dfrac{9x+5x}{135}=3\Rightarrow \dfrac{14x}{135}=3\Rightarrow x=\dfrac{405}{14}$.

7. $\dfrac{x}{3}+x+\dfrac{1}{7}=x-\dfrac{2}{6}$
   $\dfrac{2}{6}=\dfrac{1}{3}$