To solve the inequality:

\[
3^{(2x + 3)} > 3^{(3x)}
\]

Since the bases are the same (both are base 3), we can compare the exponents directly. This gives the inequality:

\[
2x + 3 > 3x
\]

Now, solve for \(x\):

1. Subtract \(2x\) from both sides:
\[
3 > x
\]

Thus, the solution to the inequality is:

\[
x < 3
\]

### Final Answer:
\[
x < 3
\]

Would you like a more detailed explanation, or do you have any questions about this?

Here are 5 related questions to consider:
1. What happens if the inequality was \(3^{(2x + 3)} \geq 3^{(3x)}\)?
2. How do we solve inequalities with different bases?
3. Can the inequality change if we include logarithms?
4. How would this inequality change if the bases were negative?
5. What if the inequality involved a base of \(e\) instead of 3?

**Tip:** When solving inequalities with the same base, comparing exponents is a useful shortcut, provided the base is positive and greater than 1.

Learn how to solve the exponential inequality 3^(2x + 3) > 3^(3x) by comparing exponents, a key concept in algebra. This step-by-step solution is ideal for students in Grades 9-11, covering important properties of exponents.

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