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.