Solve the Linear Equation: Finding X in x + 3 - 8x = 4 + 3 - x

To solve this problem, we'll follow the procedure of simplifying and solving for $x$:

• Step 1: Simplify both sides of the equation.
• Step 2: Combine like terms and move them to opposite sides to isolate $x$.
• Step 3: Solve for $x$ by performing necessary arithmetic operations.

Now, let's work through each step:

Step 1: Simplify both sides of the equation.
The given equation is $x + 3 - 8x = 4 + 3 - x$.
Combine like terms on each side:
Left side: $x - 8x + 3 = -7x + 3$
Right side: $4 - x + 3 = 7 - x$
So the equation becomes: $-7x + 3 = 7 - x$.

Step 2: Get all terms involving $x$ on one side of the equation.
Add $x$ to both sides to combine the $x$ terms:
$-7x + x + 3 = 7 - x + x$
Simplifies to: $-6x + 3 = 7$

Step 3: Solve for $x$.
Subtract 3 from both sides to isolate terms involving $x$: $-6x + 3 - 3 = 7 - 3$ $-6x = 4$
Now, divide both sides by $-6$ to solve for $x$: $x = \frac{4}{-6} = -\frac{2}{3}$

Therefore, the solution to the problem is $x = -\frac{2}{3}$.