Let's solve the equation $4x + 6 = -x + 1$.

Step 1: Combine like terms

First, move all the terms involving $x$ to one side and the constants to the other side.

$4x + x = 1 - 6$

This simplifies to:

$5x = -5$

Step 2: Solve for $x$

Now, divide both sides by 5 to isolate $x$:

$x = \frac{-5}{5} = -1$

Solution:

The solution is $x = -1$.

Do you want more details or have any questions?

Here are some related problems:

1. Solve $5x - 2 = -x + 10$.
2. Solve $2x + 7 = 5x - 3$.
3. Solve $6x + 4 = -2x + 9$.
4. Solve $3x - 5 = x + 11$.
5. Solve $8x + 3 = 2x - 7$.

Tip: Always simplify the equation step by step, combining like terms first to make the problem easier.