Solve the equation $-8(x - 3) + 2 = 7(x + 6)$ for $x$.

1. Problem Description

Solve the equation $-8(x - 3) + 2 = 7(x + 6)$ for $x$.

2. Solution Steps

We start by distributing the constants across the parentheses:

$-8(x - 3) + 2 = 7(x + 6)$

$-8x + 24 + 2 = 7x + 42$

$-8x + 26 = 7x + 42$

Now, we want to isolate $x$. Add $8x$ to both sides of the equation:

$-8x + 26 + 8x = 7x + 42 + 8x$

$26 = 15x + 42$

Subtract 42 from both sides:

$26 - 42 = 15x + 42 - 42$

$-16 = 15x$

Now, divide by 15 to solve for $x$:

$\frac{-16}{15} = \frac{15x}{15}$

$x = -\frac{16}{15}$

3. Final Answer

$x = -\frac{16}{15}$