The problem is to solve the equation $7(x+1)+4 = -6(x-7)-10$ for $x$.

1. Problem Description

The problem is to solve the equation $7(x+1)+4 = -6(x-7)-10$ for $x$.

2. Solution Steps

First, distribute the constants into the parentheses on both sides of the equation:

$7x + 7 + 4 = -6x + 42 - 10$

Combine like terms on each side:

$7x + 11 = -6x + 32$

Add $6x$ to both sides:

$7x + 6x + 11 = -6x + 6x + 32$

$13x + 11 = 32$

Subtract 11 from both sides:

$13x + 11 - 11 = 32 - 11$

$13x = 21$

Divide both sides by 13:

$\frac{13x}{13} = \frac{21}{13}$

$x = \frac{21}{13}$

3. Final Answer

$x = \frac{21}{13}$