https://file.aiquickdraw.com/mathbot/file/1726595636020o69pyv0f.jpg

Let's analyze the provided steps and find where the error occurred:

### Given Expression:
\[
(f + f + 10) - (7f - 3)
\]

### Step 1:
\[
(2f + 10) - (7f - 3)
\]

This is a correct step. The two \( f \)'s inside the parentheses are combined correctly to give \( 2f \).

### Step 2:
\[
2f + 10 - 7f - 3
\]

This is also correct. The subtraction of the second term is properly distributed over the parentheses.

### Step 3:
\[
2f - 7f + 10 - 3
\]

This step is also correct; the terms are just rearranged to group like terms.

### Step 4:
\[
-5f + 10 - 3
\]

This is correct as well. \( 2f - 7f \) gives \( -5f \).

### Step 5:
\[
-5f + 7
\]

This step is correct because \( 10 - 3 \) equals \( 7 \).

---

### Answer to Each Question:

a. **What step did the error occur at?**  
There is no error in the given steps. All steps are correct.

b. **Describe the mistake that was made.**  
There is no mistake in the work shown. The solution process is correct from start to finish.

c. **Describe all the work needed to get to the correct solution.**  
Here’s a step-by-step explanation:
1. Combine the \( f \)'s inside the parentheses: \( f + f = 2f \), leading to \( (2f + 10) - (7f - 3) \).
2. Distribute the subtraction across the second group of terms: \( 2f + 10 - 7f + 3 \).
3. Combine like terms: \( 2f - 7f = -5f \) and \( 10 - 3 = 7 \), leading to the final expression \( -5f + 7 \).

d. **What is the correct answer?**  
The correct simplified answer is:
\[
-5f + 7
\]

---

Would you like further details or have any additional questions?

### Relative Questions:
1. How would you solve similar expressions involving multiple variables?
2. What is the process for distributing subtraction over parentheses?
3. How do you identify like terms in a complex expression?
4. How can you check if an algebraic simplification is correct?
5. What are the common mistakes made when distributing terms?

### Tip:
Always double-check the distribution of negative signs when working with parentheses.

Learn how to simplify the algebraic expression (f + f + 10) - (7f - 3) with a detailed step-by-step solution. This problem involves key algebraic concepts like combining like terms and distributing subtraction over parentheses. Suitable for students in Grades 6-8.

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