Let's solve the equation step by step:

Given equation:

\[
3(x - 1) + 2(3x + 1) = -3x - 3
\]

### Step 1: Distribute the constants

\[
3(x - 1) = 3x - 3
\]
\[
2(3x + 1) = 6x + 2
\]

So the equation becomes:

\[
3x - 3 + 6x + 2 = -3x - 3
\]

### Step 2: Combine like terms on the left side

\[
(3x + 6x) - 3 + 2 = -3x - 3
\]
\[
9x - 1 = -3x - 3
\]

### Step 3: Add \(3x\) to both sides to move all terms involving \(x\) to one side

\[
9x + 3x - 1 = -3x + 3x - 3
\]
\[
12x - 1 = -3
\]

### Step 4: Add 1 to both sides to isolate the term with \(x\)

\[
12x - 1 + 1 = -3 + 1
\]
\[
12x = -2
\]

### Step 5: Divide by 12 to solve for \(x\)

\[
x = \frac{-2}{12}
\]
\[
x = \frac{-1}{6}
\]

So, the solution is:

\[
x = -\frac{1}{6}
\]

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

Here are 5 related questions you might find interesting:
1. How would the solution change if the equation was \(3(x-1) + 2(3x+1) = 3x + 3\)?
2. What is the general process for solving equations with variables on both sides?
3. How can you check your solution to make sure it is correct?
4. How would you solve the equation if the constant on the right side was different?
5. What happens if you have a quadratic term instead of a linear term?

**Tip:** Always double-check your solution by substituting it back into the original equation. This helps ensure that no mistakes were made during the process.

Learn how to solve the equation 3(x-1) + 2(3x+1) = -3x-3 with detailed step-by-step solutions. This problem involves algebraic concepts such as equations, distributive property, and solving linear equations. Suitable for Grades 7-9.

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