https://file.aiquickdraw.com/mathbot/file/1725532078570mlvrn8xc.jpg

The inequality provided in the image is:

\[
x^2 > \frac{72}{x}
\]

### Step-by-step solution:

1. **Multiply both sides of the inequality by \(x\)** to eliminate the fraction (assuming \(x \neq 0\)):
   \[
   x^3 > 72
   \]

2. **Solve for \(x\)** by taking the cube root of both sides:
   \[
   x > \sqrt[3]{72}
   \]

   The cube root of 72 is approximately 4.16. So:

   \[
   x > 4.16
   \]

### Final result:
The solution set consists of all \(x\) such that \(x > \sqrt[3]{72}\).

Would you like more details or have any questions on this solution?

### Follow-up questions:
1. What is the cube root of 72 to more decimal places?
2. How would the solution change if the inequality were \(x^2 \geq \frac{72}{x}\)?
3. How do you solve this inequality graphically?
4. What are the restrictions on \(x\) in this type of inequality?
5. How do you solve similar inequalities involving higher powers of \(x\)?

**Tip:** Always check the domain of the variable when solving inequalities involving fractions.

The set of solutions of the inequality x^2 > 72/x consists of all x with

Explore how to solve the inequality x^2 > 72/x by multiplying both sides, solving for x, and understanding the solution set. This algebra problem is ideal for high school students in Grades 9-12.

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