To solve the equation $-4x + 3 = x + 4$, follow these steps:

1. Move the variable terms to one side:
   Subtract $x$ from both sides of the equation to get all the $x$ terms on one side: $-4x - x + 3 = 4$ Simplify: $-5x + 3 = 4$

2. Move the constant terms to the other side:
   Subtract 3 from both sides to isolate the term with $x$: $-5x = 4 - 3$ Simplify: $-5x = 1$

3. Solve for $x$:
   Divide both sides by $-5$: $x = \frac{1}{-5}$ Simplify: $x = -\frac{1}{5}$

So, the solution is $x = -\frac{1}{5}$.

Would you like any details or have any questions?

Here are five related questions you might find useful:

1. How do you solve linear equations with fractions?
2. What is the process for solving equations with variables on both sides?
3. How do you solve inequalities that are similar to linear equations?
4. How do you check if your solution to a linear equation is correct?
5. What happens when a linear equation has no solution or infinitely many solutions?

Tip: Always remember to simplify your equation at each step to make solving easier!