Let's solve the equation $4x + 1 = 6 - 5x$ step by step and verify if the solution is indeed $\frac{5}{9}$.

Steps:

1. Move all terms involving $x$ to one side: $4x + 5x = 6 - 1$ This simplifies to: $9x = 5$

2. Solve for $x$: $x = \frac{5}{9}$

So yes, the solution to the equation is indeed $\frac{5}{9}$.

Would you like more details on this, or do you have any other questions?

Here are some related questions for further practice:

1. Solve $3x + 2 = 7 - 4x$.
2. Solve $5x - 3 = 2x + 8$.
3. Solve $7x + 4 = 12 - 6x$.
4. Solve $2(x + 3) = 4 - 3x$.
5. Solve $10x - 7 = 5x + 14$.

Tip: Always group terms with variables on one side and constants on the other to simplify linear equations easily.