To simplify the given expression:

\[
-\frac{1}{3}(9y - 12) + 5y
\]

### Step 1: Distribute \(-\frac{1}{3}\) to both terms inside the parentheses:

\[
-\frac{1}{3} \times 9y = -3y
\]
\[
-\frac{1}{3} \times -12 = 4
\]

So, the expression becomes:

\[
-3y + 4 + 5y
\]

### Step 2: Combine like terms:
\(-3y\) and \(5y\) are like terms:

\[
-3y + 5y = 2y
\]

Thus, the expression simplifies to:

\[
2y + 4
\]

This is the simplified form.

Would you like further details or have any questions?

### Relative Questions:
1. What happens when you distribute a negative fraction over terms inside parentheses?
2. How do you combine like terms with different signs?
3. How would you handle this expression if more variables were involved?
4. What if there were exponents on the \(y\) terms—how would that change the solution?
5. How does factoring apply when simplifying expressions?

### Tip:
Always distribute multiplication over addition or subtraction before combining like terms to simplify an expression accurately.

Learn how to simplify the expression -1/3(9y - 12) + 5y step-by-step. This problem covers algebraic concepts such as simplifying expressions, using the distributive property, and combining like terms. Suitable for students in Grades 7-9.

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