$$\frac{1}{4}\times 2+\frac{1}{4}\left(-1\right)x+\frac{3}{2}=3\left(x-2\right)$$
Multiply $\frac{1}{4}$ and $2$ to get $\frac{2}{4}$.$$\frac{2}{4}+\frac{1}{4}\left(-1\right)x+\frac{3}{2}=3\left(x-2\right)$$
Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.$$\frac{1}{2}+\frac{1}{4}\left(-1\right)x+\frac{3}{2}=3\left(x-2\right)$$
Multiply $\frac{1}{4}$ and $-1$ to get $-\frac{1}{4}$.$$\frac{1}{2}-\frac{1}{4}x+\frac{3}{2}=3\left(x-2\right)$$
Since $\frac{1}{2}$ and $\frac{3}{2}$ have the same denominator, add them by adding their numerators.$$\frac{1+3}{2}-\frac{1}{4}x=3\left(x-2\right)$$
Add $1$ and $3$ to get $4$.$$\frac{4}{2}-\frac{1}{4}x=3\left(x-2\right)$$
Divide $4$ by $2$ to get $2$.$$2-\frac{1}{4}x=3\left(x-2\right)$$
Use the distributive property to multiply $3$ by $x-2$.$$2-\frac{1}{4}x=3x-6$$
Subtract $3x$ from both sides.$$2-\frac{1}{4}x-3x=-6$$
Combine $-\frac{1}{4}x$ and $-3x$ to get $-\frac{13}{4}x$.$$2-\frac{13}{4}x=-6$$
Subtract $2$ from both sides.$$-\frac{13}{4}x=-6-2$$
Subtract $2$ from $-6$ to get $-8$.$$-\frac{13}{4}x=-8$$
Multiply both sides by $-\frac{4}{13}$, the reciprocal of $-\frac{13}{4}$.$$x=-8\left(-\frac{4}{13}\right)$$
Express $-8\left(-\frac{4}{13}\right)$ as a single fraction.$$x=\frac{-8\left(-4\right)}{13}$$
Multiply $-8$ and $-4$ to get $32$.$$x=\frac{32}{13}$$