We are asked to solve the equation $4(x-9) = 7(x+7)$ for $x$.

1. Problem Description

We are asked to solve the equation $4(x-9) = 7(x+7)$ for $x$.

2. Solution Steps

We first distribute the numbers on both sides of the equation:

$4x - 36 = 7x + 49$

Next, we subtract $4x$ from both sides:

$-36 = 3x + 49$

Then, subtract 49 from both sides:

$-36 - 49 = 3x$

$-85 = 3x$

Finally, divide by 3 to isolate $x$:

$x = \frac{-85}{3}$

3. Final Answer

$x = -\frac{85}{3}$