Let's solve the equation step by step to find the value of $a$.

Given equation:

$a + 3(a - 1) = 3(2 + 1)$

Step 1: Simplify the right-hand side

First, simplify the expression on the right-hand side:

$3(2 + 1) = 3 \times 3 = 9$

So, the equation becomes:

$a + 3(a - 1) = 9$

Step 2: Distribute the 3 on the left-hand side

Next, distribute the 3 over the expression $(a - 1)$:

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

So, the equation is now:

$a + 3a - 3 = 9$

Step 3: Combine like terms

Combine the terms involving $a$ on the left-hand side:

$4a - 3 = 9$

Step 4: Isolate the variable

Add 3 to both sides of the equation to eliminate the constant on the left-hand side:

$4a = 12$

Step 5: Solve for $a$

Finally, divide both sides by 4:

$a = \frac{12}{4} = 3$

Justification:

We have solved the equation using standard algebraic operations, including simplifying both sides, distributing, combining like terms, and isolating the variable. The final value of $a$ is 3.

Do you want details or have any questions?

Here are 5 relative questions that expand on this concept:

1. What are the steps to simplify an equation with multiple parentheses?
2. How can we check if the solution to an equation is correct?
3. What are like terms, and how do you combine them in an equation?
4. How do you handle equations with variables on both sides?
5. Can you solve for other variables if the equation has more than one?

Tip: Always check your final answer by substituting the variable back into the original equation!