jmc

Since subtracting a term is the same as adding the negative, we have $x+[-2(1+x)]+3(1-x)+[-4(1+2x)]$. Now, we can distribute several terms and negative signs. We have $-2(1+x)=-2-2x$, and $-4(1+2x)=-4-8x$. Also, $3(1-x)=3-3x$.

Substituting for these simplified expressions, we get $x+(-2-2x)+(3-3x)+(-4-8x)$. Next, we can group together similar terms by separating constants from the variable $x$. So, we have $(x-2x-3x-8x)+(-2+3-4)=(-12x)+(-3)$. This yields $\boxed{-12x-3}$.