Solve for X in the Equation: -8x + x - 5 + 3x = 4 - 3 - 1 + 6x

To solve the equation $-8x + x - 5 + 3x = 4 - 3 - 1 + 6x$, follow these steps:

• Step 1: Simplify each side by combining like terms.
• Step 2: Rearrange the equation to isolate $x$.
• Step 3: Solve for $x$.

Let's solve the problem step-by-step:

Step 1: Simplify each side.

On the left side, combine the like terms $-8x + x + 3x$:

$-8x + x + 3x = -8x + 4x = -4x$

Thus, the left side becomes:

$-4x - 5$

On the right side, compute the constant terms first:

$4 - 3 - 1 = 0$

Therefore, the right side simplifies to:

$0 + 6x = 6x$

Now the equation is:

$-4x - 5 = 6x$

Step 2: Move all terms involving $x$ to one side.

Add $4x$ to both sides to move the variable terms together:

$-4x + 4x - 5 = 6x + 4x$

This simplifies to:

$-5 = 10x$

Step 3: Solve for $x$.

Divide both sides by 10:

$x = \frac{-5}{10}$

Thus, simplifying the fraction, we have:

$x = -\frac{1}{2}$

Therefore, the solution to the equation is $x = -\frac{1}{2}$, corresponding to choice 3.