The problem is to solve the linear equation $-3x + 2 = -10x - 5$ for $x$.

1. Problem Description

The problem is to solve the linear equation $-3x + 2 = -10x - 5$ for $x$.

2. Solution Steps

We want to isolate $x$ on one side of the equation.

First, we add $10x$ to both sides of the equation:

$-3x + 2 + 10x = -10x - 5 + 10x$

$7x + 2 = -5$

Next, we subtract 2 from both sides of the equation:

$7x + 2 - 2 = -5 - 2$

$7x = -7$

Finally, we divide both sides of the equation by 7:

$\frac{7x}{7} = \frac{-7}{7}$

$x = -1$

3. Final Answer

The solution is $x = -1$.