Let's solve the equation step by step:

Given equation:
\[
3y + 3(2y - 5) - 5[3(y - 1)] = 12
\]

### Step 1: Distribute the constants inside the parentheses.

1. Distribute the \(3\) in \(3(2y - 5)\):
   \[
   3 \times 2y - 3 \times 5 = 6y - 15
   \]

2. Distribute the \(-5\) in \(-5[3(y - 1)]\):
   \[
   -5 \times 3 \times (y - 1) = -15(y - 1)
   \]
   Distribute \(-15\) inside the parentheses:
   \[
   -15y + 15
   \]

So the equation becomes:
\[
3y + 6y - 15 - 15y + 15 = 12
\]

### Step 2: Combine like terms.

Combine all the \(y\) terms and the constant terms:
\[
(3y + 6y - 15y) + (-15 + 15) = 12
\]
\[
-6y = 12
\]

### Step 3: Solve for \(y\).

Divide both sides by \(-6\) to isolate \(y\):
\[
y = \frac{12}{-6} = -2
\]

So, the solution is:
\[
y = -2
\]

Would you like more details or have any questions about this solution?

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Here are 5 related questions you might find interesting:

1. How would the equation change if the constant 12 on the right side were doubled?
2. What would be the effect on the solution if the term \(-15y\) was instead \(+15y\)?
3. Can you solve a similar equation but with a different constant term on the right-hand side?
4. What happens if you set up a system of equations using this equation and another linear equation?
5. How does the distributive property help in solving equations like this?

**Tip:** Always remember to combine like terms after distribution to simplify the equation and avoid mistakes.

Learn how to solve the linear equation 3y + 3(2y – 5) – 5[3(y - 1)] = 12 with a detailed step-by-step solution. This problem involves using the distributive property and combining like terms. Suitable for students in Grades 7-9.

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