Let's analyze and solve the equations step by step from the image.

1. Equation 1: $4 + (\_ + 1) = \_ = 9 + (4 + 1)$ The right-hand side simplifies as: $9 + (4 + 1) = 9 + 5 = 14$ Therefore, the left-hand side must also equal 14. This means: $4 + (\_ + 1) = 14 \implies \_ + 1 = 10 \implies \_ = 9$ Hence, the first equation is: $4 + (9 + 1) = 14 = 9 + (4 + 1)$

2. Equation 2: $7 + (4 + \_) = 19 = 8 + (4 + \_)$ From the right-hand side: $8 + (4 + \_) = 19 \implies 4 + \_ = 11 \implies \_ = 7$ Substituting this back, we have: $7 + (4 + 7) = 19$

3. Equation 3: $7 + (6 + 5) = \_ = 5 + (\_ + \_)$ First, let's compute the left-hand side: $7 + (6 + 5) = 7 + 11 = 18$ Therefore, the right-hand side should also equal 18: $5 + (\_ + \_) = 18$ Solving this, we get: $\_ + \_ = 13$ One possible solution is $\_ = 6$ and $\_ = 7$.

4. Equation 4: $1 + (1 + 5) = \_ = 9 + (\_ + \_)$ The left-hand side simplifies to: $1 + (1 + 5) = 1 + 6 = 7$ Therefore, the right-hand side should also equal 7: $9 + (\_ + \_) = 7$ This implies: $\_ + \_ = -2$ One possible solution is $\_ = -1$ and $\_ = -1$.

Would you like to discuss any step in more detail or need clarification on the solution?

Here are some follow-up questions:

1. How do you approach solving equations with multiple unknowns?
2. What is the significance of balancing both sides of an equation?
3. Can you create another equation similar to those in the image?
4. How does adding parentheses change the order of operations in equations?
5. What are other ways to simplify complex expressions?

Tip: When solving equations, always simplify both sides and isolate the unknown variables step by step.