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Let's solve the equation step-by-step to determine if it has exactly one solution:

The given equation is:
\[
13b + 7 = 9b - 33 + 4b
\]

### Step 1: Combine like terms on the right-hand side
On the right-hand side, combine \( 9b \) and \( 4b \):
\[
9b + 4b = 13b
\]
Thus, the equation becomes:
\[
13b + 7 = 13b - 33
\]

### Step 2: Subtract \( 13b \) from both sides
To simplify further, subtract \( 13b \) from both sides:
\[
13b + 7 - 13b = 13b - 33 - 13b
\]
This simplifies to:
\[
7 = -33
\]

### Step 3: Analyze the result
Since \( 7 \neq -33 \), we have a contradiction. This means that the equation has no solutions.

### Conclusion:
The equation does **not** have exactly one solution; it has **no solution**. So, the correct answer is "no."

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. What are the different types of solutions a linear equation can have?
2. How do you know when a linear equation has no solutions?
3. What is the difference between having no solution and infinite solutions?
4. Can you show how to solve an equation that does have exactly one solution?
5. How would you solve an equation with variables on both sides?

**Tip:** When simplifying equations, always check for contradictions or identities to determine if the equation has no solution or infinite solutions.

Does this equation have exactly one solution? 13b + 7 = 9b - 33 + 4b

Explore how to determine if the linear equation 13b + 7 = 9b - 33 + 4b has exactly one solution. Learn step-by-step how combining like terms and identifying contradictions can show that an equation has no solution. Suitable for students in Grades 8-10.

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