To solve the inequality:

\[
9p > 14p - 18
\]

### Step-by-step solution:

1. **Subtract \(14p\) from both sides** to move the \(p\)-terms to one side:

   \[
   9p - 14p > -18
   \]

   Simplifying the left-hand side:

   \[
   -5p > -18
   \]

2. **Divide both sides by \(-5\)**. Remember, when you divide by a negative number, the inequality sign flips:

   \[
   p < \frac{-18}{-5}
   \]

   Simplifying the fraction:

   \[
   p < 3.6
   \]

### Final answer:
\[
p < 3.6
\]

Would you like further details or explanations on any step?

Here are some related questions you might find helpful:

1. How do you solve inequalities involving fractions?
2. What happens when multiplying or dividing inequalities by negative numbers?
3. How do you solve a system of inequalities?
4. Can inequalities be graphed on a number line?
5. How do you solve quadratic inequalities?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the linear inequality 9p > 14p - 18 with a detailed step-by-step solution. This problem covers key algebraic concepts, including subtracting terms and dividing inequalities by negative numbers. Suitable for students in Grades 7-9.

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