Solve for X: Linear Equation 3-4(x-2)=6x+4(3-x)

Let's solve the equation $3-4(x-2)=6x+4(3-x)$.

First, apply the distributive property on both sides:

• For the left side: $3 - 4(x - 2)$ becomes $3 - 4x + 8$, which simplifies to $11 - 4x$.
• For the right side: $6x + 4(3 - x)$ becomes $6x + 12 - 4x$, which simplifies to $2x + 12$.

Now the equation is:

$11 - 4x = 2x + 12$

Combine like terms to isolate $x$. First, move all terms containing $x$ to one side and constant terms to the other side:

• Add $4x$ to both sides: $11 = 6x + 12$.
• Subtract 12 from both sides: $11 - 12 = 6x$, which simplifies to $-1 = 6x$.

Finally, solve for $x$ by dividing both sides by 6:

$x = -\frac{1}{6}$.

Therefore, the solution to the problem is $x = -\frac{1}{6}$, which corresponds to choice 4.