Let's solve the equation step by step:

Given:

$6 - 3(a - 1) = 5 + a$

Step 1: Distribute the -3 to both terms inside the parentheses.

$6 - 3a + 3 = 5 + a$

Step 2: Combine like terms on the left side.

$9 - 3a = 5 + a$

Step 3: Move all the terms involving $a$ to one side and the constants to the other side.

First, subtract $a$ from both sides:

$9 - 3a - a = 5$

This simplifies to:

$9 - 4a = 5$

Step 4: Move the constant 9 to the right side by subtracting 9 from both sides:

$-4a = 5 - 9$

$-4a = -4$

Step 5: Solve for $a$ by dividing both sides by -4:

$a = \frac{-4}{-4}$

$a = 1$

Final Answer:

$\boxed{a = 1}$

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Would you like any further details on how to solve this?

Here are some related questions for further practice:

1. Solve $4 - 2(x - 3) = 10 + x$.
2. What is the solution to the equation $7 + 2b = 4(b + 5)$?
3. If $2x - 3 = 5 + 3(x + 1)$, find the value of $x$.
4. Solve $5(2 - 3a) = 3a + 8$.
5. If $6a - 4 = 2(3a + 2)$, determine $a$.

Tip: Always remember to distribute first and combine like terms before isolating the variable!