Solve for X: Simplify and Balance the Equation -8x + 5(3-x) = 6 - 4x + 3(x+1)

To solve this problem, we'll follow these steps:

• Step 1: Apply the distributive property to both sides.
• Step 2: Combine like terms on each side.
• Step 3: Move all terms involving $x$ to one side and constants to the other.
• Step 4: Simplify to solve for $x$.

Now, let's work through each step:

Step 1: Distribute on the left: $5(3-x) = 15 - 5x$. So, the left side becomes $-8x + 15 - 5x$.
Distribute on the right: $3(x+1) = 3x + 3$. So, the right side becomes $6 - 4x + 3x + 3$.

Step 2: Combine the like terms:
Left side: $-8x - 5x + 15 = -13x + 15$.
Right side: $6 + 3 + 3x - 4x = 9 - x$.

Step 3: Equating both sides, we have:
$-13x + 15 = 9 - x$.

Move all $x$-terms to one side and constant terms to the other:
Add $13x$ to both sides:
$15 = 9 + 12x$.

Step 4: Isolate $x$ by subtracting 9 from both sides:
$6 = 12x$.
Divide both sides by 12:
$x = \frac{6}{12} = \frac{1}{2}$.

Therefore, the solution to the equation is $x = \frac{1}{2}$, which corresponds to choice 2.