Let's solve the equation step by step.

Given the equation:

$4x + 7 = 5x + 11$

Step 1: Subtract $4x$ from both sides to isolate the terms involving $x$ on one side:

$7 = 5x - 4x + 11$

$7 = x + 11$

Step 2: Subtract 11 from both sides to solve for $x$:

$7 - 11 = x$

$-4 = x$

So, the value of $x$ is $-4$.

Would you like more details on this solution or have any questions?

Here are 5 related questions:

1. How would you solve $3y + 2 = 4y + 10$ for $y$?
2. Can you solve $2x + 5 = 3x + 12$ and find the value of $x$?
3. What happens if you have to solve $6x + 4 = 5x + 9$?
4. How would you approach solving an equation with variables on both sides?
5. What if the equation was $4x + 7 = 5x - 3$? How would that change the solution?

Tip: When solving linear equations, always try to move the variables to one side and the constants to the other to simplify your work.