**How many solutions does the following equation have?**

\[3(y+9)=12y+13\]

Choose 1 answer:

Choose 1 answer:

(Choice A)   

No solutions

A

No solutions

(Choice B)   

Exactly one solution

B

Exactly one solution

(Choice C)   

Infinitely many solutions

C

Infinitely many solutions

Let's solve the equation \(3(y + 9) = 12y + 13\) step by step to determine how many solutions it has.

### Step 1: Expand the left side
Distribute the 3 on the left side of the equation:
\[
3(y + 9) = 3y + 27
\]
Now, the equation becomes:
\[
3y + 27 = 12y + 13
\]

### Step 2: Move the variable terms to one side
Subtract \(3y\) from both sides to get the variable on one side:
\[
27 = 9y + 13
\]

### Step 3: Move the constant terms to the other side
Subtract 13 from both sides:
\[
14 = 9y
\]

### Step 4: Solve for \(y\)
Divide both sides by 9:
\[
y = \frac{14}{9}
\]

### Conclusion:
The equation has exactly one solution, which is \(y = \frac{14}{9}\).

The correct answer is:
- **Choice B: Exactly one solution**

Would you like further details on this solution or any other questions?

Here are 5 related questions:
1. What are the steps to solve a linear equation?
2. How do you check if your solution is correct in an equation?
3. Can linear equations have more than one solution?
4. What happens when both sides of an equation are the same after simplification?
5. How do you interpret the result when an equation simplifies to a false statement?

**Tip:** Always perform a final check by substituting your solution back into the original equation to verify its correctness.

Learn how to solve the linear equation 3(y+9)=12y+13 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equation solving techniques. Suitable for students in Grades 7-9.

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