https://file.aiquickdraw.com/mathbot/file/1727452424696id34l4gm.jpg

The equation displayed in the image is:

\[
2y - 3 = 12y + 27
\]

Let's solve this equation step by step.

### Step 1: Simplify both sides
First, subtract \(12y\) from both sides to bring all terms involving \(y\) to the left side:

\[
2y - 12y - 3 = 27
\]

This simplifies to:

\[
-10y - 3 = 27
\]

### Step 2: Isolate the variable \(y\)
Next, add 3 to both sides:

\[
-10y = 30
\]

### Step 3: Solve for \(y\)
Divide both sides by \(-10\):

\[
y = \frac{30}{-10} = -3
\]

### Step 4: Verify the solution
Substitute \(y = -3\) into the original equation to check if it holds true:

\[
2(-3) - 3 = 12(-3) + 27
\]

Simplifying both sides:

\[
-6 - 3 = -36 + 27
\]

\[
-9 = -9
\]

Since both sides are equal, the solution is correct.

### Conclusion:
The solution set is \(\{-3\}\), which corresponds to option A.

Would you like further clarification or details on any of these steps? 

Here are 5 related questions:
1. How would the solution change if the equation was \(2y - 3 = 12y - 27\)?
2. What is the solution if the right-hand side of the equation includes a constant term of 0?
3. How do you solve an equation where the variable appears on both sides with fractions?
4. How does one verify a solution in more complex equations?
5. How would the equation behave if the coefficients were non-integer values?

**Tip:** Always check your solution by substituting it back into the original equation to ensure accuracy.

Solve the equation 2y - 3 = 12y + 27. What is the solution set?

Learn how to solve the linear equation 2y - 3 = 12y + 27 with a detailed step-by-step solution. This problem involves simplifying and isolating the variable y. Suitable for students in Grades 6-8.

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