To solve the inequality \( p + 1 < 3p + 5 \), follow these steps:

1. Start by subtracting \( p \) from both sides of the inequality to simplify:
   \[
   1 < 2p + 5
   \]

2. Next, subtract 5 from both sides:
   \[
   1 - 5 < 2p
   \]
   \[
   -4 < 2p
   \]

3. Finally, divide both sides by 2 to solve for \( p \):
   \[
   \frac{-4}{2} < p
   \]
   \[
   -2 < p
   \]

Thus, the solution is \( p > -2 \).

### Final Answer:
\[
p > -2
\]

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How would the inequality change if the signs were reversed?
2. What happens to the inequality if you multiply both sides by a negative number?
3. Can you graph the solution \( p > -2 \) on a number line?
4. How does solving an inequality differ from solving an equation?
5. How would you handle a similar inequality with variables on both sides?

**Tip:** When multiplying or dividing both sides of an inequality by a negative number, always remember to reverse the inequality sign.

Learn how to solve the linear inequality p + 1 < 3p + 5 with a detailed, step-by-step solution. This problem focuses on solving inequalities and algebraic manipulations, suitable for students in Grades 6-8.

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