We need to solve the equation $7(x+1) = 9 - (2x-1)$ for $x$.

1. Problem Description

We need to solve the equation $7(x+1) = 9 - (2x-1)$ for $x$.

2. Solution Steps

First, we distribute the $7$ on the left side and the negative sign on the right side of the equation:

$7(x+1) = 7x + 7$

$9 - (2x - 1) = 9 - 2x + 1 = 10 - 2x$

So the equation becomes:

$7x + 7 = 10 - 2x$

Next, we add $2x$ to both sides of the equation:

$7x + 2x + 7 = 10 - 2x + 2x$

$9x + 7 = 10$

Then, we subtract $7$ from both sides of the equation:

$9x + 7 - 7 = 10 - 7$

$9x = 3$

Finally, we divide both sides of the equation by $9$:

$\frac{9x}{9} = \frac{3}{9}$

$x = \frac{1}{3}$

3. Final Answer

$x = \frac{1}{3}$