Solve:

$\dfrac{1}{10} - \dfrac{7}{x} = 35$

$\dfrac{1}{10} - \dfrac{7}{x} = 35\\[1em] ⇒ \dfrac{7}{x} = \dfrac{1}{10} - 35\\[1em] ⇒ \dfrac{7}{x} = \dfrac{1}{10} - \dfrac{35}{1}$

Since L.C.M. of denominators 10 and 1 = 10, multiply each term with 10 to get:

$⇒ \dfrac{7 \times 10}{x} = \dfrac{1 \times 10}{10} - \dfrac{35 \times 10}{1}\\[1em] ⇒ \dfrac{70}{x} = 1 - 350\\[1em] ⇒ \dfrac{70}{x} = - 349\\[1em] ⇒ x = - \dfrac{70}{349}$

Hence, the value of x is $-\dfrac{70}{349}$.