Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $10x$, the least common multiple of $x,10$.
$$10\times 7+10x\times 35=x$$
Multiply $10$ and $7$ to get $70$.
$$70+10x\times 35=x$$
Multiply $10$ and $35$ to get $350$.
$$70+350x=x$$
Subtract $x$ from both sides.
$$70+350x-x=0$$
Combine $350x$ and $-x$ to get $349x$.
$$70+349x=0$$
Subtract $70$ from both sides. Anything subtracted from zero gives its negation.
$$349x=-70$$
Divide both sides by $349$.
$$x=\frac{-70}{349}$$
Fraction $\frac{-70}{349}$ can be rewritten as $-\frac{70}{349}$ by extracting the negative sign.
