Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $4x$, the least common multiple of $4x,4,2$.
$$1+4x\left(-\frac{1}{4}\right)=2x$$
Multiply $4$ and $-\frac{1}{4}$ to get $-1$.
$$1-x=2x$$
Subtract $2x$ from both sides.
$$1-x-2x=0$$
Combine $-x$ and $-2x$ to get $-3x$.
$$1-3x=0$$
Subtract $1$ from both sides. Anything subtracted from zero gives its negation.
$$-3x=-1$$
Divide both sides by $-3$.
$$x=\frac{-1}{-3}$$
Fraction $\frac{-1}{-3}$ can be simplified to $\frac{1}{3}$ by removing the negative sign from both the numerator and the denominator.
