https://file.aiquickdraw.com/mathbot/file/1724968157494jfhnvl8j.jpg

Let's solve the inequality step by step.

The given inequality is:
\[
3(5 - y) + 3y > 12
\]

### Step 1: Distribute the 3 across the terms inside the parentheses
\[
3 \times 5 - 3 \times y + 3y > 12
\]
\[
15 - 3y + 3y > 12
\]

### Step 2: Simplify the equation
Notice that the \(-3y\) and \(+3y\) cancel each other out:
\[
15 > 12
\]

### Step 3: Interpret the result
The inequality \(15 > 12\) is always true. This means that the inequality is true for any value of \(y\). Therefore, the correct answer is:

- **No solution** is incorrect because there are indeed solutions.
- **\(y <\) (some value)** is incorrect because \(y\) can be any value.
- **\(y >\) (some value)** is also incorrect for the same reason.

### Conclusion:
Since the inequality holds for all values of \(y\), the correct option is:
- **All real numbers satisfy the inequality** (though this option isn't explicitly listed in the image, it's the correct interpretation).

Would you like more details or have any questions?

### Related Questions:
1. What happens if the inequality were \(3(5 - y) + 3y \geq 12\)?
2. How would you solve the inequality if there was a different coefficient for \(y\)?
3. What is the significance of an inequality that is always true?
4. How can you graphically represent the solutions to this inequality?
5. What if the inequality was \(3(5 - y) + 3y < 12\)? How would that change the solution?

### Tip:
When simplifying inequalities, always check if terms cancel out, as it can simplify your solution process.

Learn how to solve the inequality 3(5 - y) + 3y > 12 with a detailed step-by-step solution. Understand the simplification of inequalities and how to interpret the results. Suitable for students in Grades 7-9 studying algebraic inequalities.

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