https://file.aiquickdraw.com/mathbot/file/1728564488610egoy7hzl.jpg

The equation shown in the image is:

\[
gA + QA = f
\]

We are asked to solve for \( A \), ensuring that the capitalization of letters is considered. To solve this for \( A \):

### Step-by-step solution:
1. Factor \( A \) from both terms on the left-hand side:
   \[
   A(g + Q) = f
   \]

2. To isolate \( A \), divide both sides by \( g + Q \) (assuming \( g + Q \neq 0 \)):
   \[
   A = \frac{f}{g + Q}
   \]

So the solution for \( A \) is:
\[
A = \frac{f}{g + Q}
\]

Let me know if you need further clarification, details, or help with other questions!

### Related questions:
1. What happens if \( g + Q = 0 \)?
2. How do you factor expressions when there are more than two terms?
3. Can you solve this if \( A \) is already isolated on one side?
4. How does factoring help in solving multi-variable equations?
5. How can this method be applied to more complex equations?

**Tip**: Always check that the denominator in your solution is not equal to zero, as this would make the expression undefined!

Solve the following equation for A: gA + QA = f. Be sure to take into account whether a letter is capitalized or not.

Learn how to solve the literal equation gA + QA = f for A with a step-by-step solution. This problem focuses on factoring and algebraic manipulation, suitable for students in Grades 8-10.

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