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The equation given is:

\[
A = P(1 + nr)
\]

We are tasked with solving for the variable \(n\). Here's how we can do that:

### Step-by-step solution:

1. **Start with the original equation:**

   \[
   A = P(1 + nr)
   \]

2. **Divide both sides by \(P\) to isolate the term with \(n\):**

   \[
   \frac{A}{P} = 1 + nr
   \]

3. **Subtract 1 from both sides:**

   \[
   \frac{A}{P} - 1 = nr
   \]

4. **Solve for \(n\) by dividing both sides by \(r\):**

   \[
   n = \frac{\frac{A}{P} - 1}{r}
   \]

Thus, the solution for \(n\) is:

\[
n = \frac{\frac{A}{P} - 1}{r}
\]

Let me know if you'd like any further clarifications!

---

Here are five related questions:

1. How does this formula change if you are solving for \(P\) instead of \(n\)?
2. What is the interpretation of each variable in the context of simple interest?
3. How would the equation change if compounded interest was used instead of simple interest?
4. If \(A\), \(P\), and \(r\) are known, how can you calculate the exact value of \(n\)?
5. How would you solve the equation graphically for \(n\)?

### Tip:
When solving for a variable, always aim to isolate the variable step by step using inverse operations.

Learn how to solve the linear equation A = P(1 + nr) for n with a detailed step-by-step breakdown. This problem explores algebraic manipulation techniques and is suitable for students in Grades 9-12.

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