The solutions to the equations are as follows:

1. For the first equation $4(u + 1) + 5 = 6(u - 1) + u$:

   • The solution is $u = 5$.

2. For the second equation $4(w - 1) - 1 = 2(2w - 3)$:

   • There is no solution, meaning no value of $w$ satisfies the equation.

Would you like more details on the steps used to solve these, or do you have any further questions?

Here are 5 related questions to expand on the topic:

1. How do you solve linear equations with variables on both sides?
2. What does it mean when an equation has no solution?
3. Can all linear equations have solutions in real numbers?
4. How do you check if a solution to an equation is correct?
5. What is the difference between a unique solution and all real numbers being solutions?

Tip: Always simplify both sides of the equation as much as possible before solving.