To solve the equation $4x - 3 = 5x + 2$, follow these steps:

1. Subtract $4x$ from both sides to move the terms with $x$ to one side of the equation: $4x - 4x - 3 = 5x - 4x + 2$ This simplifies to: $-3 = x + 2$

2. Subtract 2 from both sides to isolate $x$: $-3 - 2 = x + 2 - 2$ This simplifies to: $-5 = x$

So, the solution is $x = -5$.

Would you like more details or have any questions?

Here are some related questions to consider:

1. How would you solve the equation $3x + 4 = 2x - 1$?
2. What happens if the equation has no solution?
3. Can you solve $6x - 3 = 4x + 9$ and explain the steps?
4. How would the solution change if the equation were $4x - 3 = 5x - 2$?
5. How can you check the solution to a linear equation?

Tip: When solving linear equations, try to simplify and combine like terms as early as possible to make the process smoother.