To solve the equation \(7p + 9 = 9p - 5\), we need to isolate the variable \(p\). Here's a step-by-step solution:

1. **Subtract \(7p\) from both sides of the equation:**

   \[
   7p + 9 - 7p = 9p - 5 - 7p
   \]

   Simplifying this, we get:

   \[
   9 = 2p - 5
   \]

2. **Add 5 to both sides of the equation:**

   \[
   9 + 5 = 2p - 5 + 5
   \]

   Simplifying this, we get:

   \[
   14 = 2p
   \]

3. **Divide both sides by 2 to solve for \(p\):**

   \[
   \frac{14}{2} = \frac{2p}{2}
   \]

   Simplifying this, we get:

   \[
   p = 7
   \]

So, the solution is \(p = 7\).

Would you like more details or have any questions?

Here are 8 related questions to expand on this topic:
1. How would you solve the equation if it was \(7p + 9 = 9p + 5\)?
2. What is the value of \(p\) if the equation was \(8p + 9 = 10p - 7\)?
3. How do you check if your solution for \(p\) is correct?
4. Can you graph the equations \(7p + 9\) and \(9p - 5\) to visually find the solution?
5. What are the steps to solve a quadratic equation?
6. How would you solve for \(p\) in the equation \(3p - 4 = 5p + 2\)?
7. Can you explain the difference between linear and quadratic equations?
8. How would you solve a system of equations involving \(p\)?

**Tip:** Always check your solution by substituting it back into the original equation to ensure both sides are equal.

Learn how to solve the equation 7p + 9 = 9p - 5 step-by-step. Understand linear equation solving with a detailed explanation and solution. Suitable for students in Grades 7-9.

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