https://file.aiquickdraw.com/mathbot/file/1726092583394i8ldg7k4.jpg

The image shows the inequality \( 150 > 710 \cdot x^{-2} \). Let's solve for \( x \).

### Step-by-step solution:

1. Start with the inequality:
   \[
   150 > 710 \cdot x^{-2}
   \]

2. To isolate \( x \), divide both sides by 710:
   \[
   \frac{150}{710} > x^{-2}
   \]

   Simplifying the left side:
   \[
   \frac{150}{710} = \frac{15}{71}
   \]

   So, we now have:
   \[
   \frac{15}{71} > x^{-2}
   \]

3. Take the reciprocal of both sides (and reverse the inequality, because reciprocals reverse inequality directions):
   \[
   x^2 > \frac{71}{15}
   \]

4. Solve for \( x \) by taking the square root of both sides:
   \[
   x > \sqrt{\frac{71}{15}}
   \]

   Simplifying:
   \[
   x > \sqrt{4.7333}
   \]

   \[
   x > 2.175
   \]

### Conclusion:
The solution to the inequality is \( x > 2.175 \).

Would you like more details or further explanation? Here are some follow-up questions you could explore:

1. How do reciprocal inequalities work in general?
2. What happens if the inequality involves a negative exponent?
3. What is the impact of squaring both sides in inequalities?
4. How can you check your solution by substituting values?
5. How does changing the coefficient \( 710 \) affect the result?

**Tip:** When dealing with inequalities involving exponents, always be careful when taking reciprocals—inequalities reverse!

Learn how to solve the inequality 150 > 710 * x^(-2) with a detailed step-by-step explanation. This problem involves exponent rules, reciprocal properties, and solving inequalities. Suitable for high school students (Grades 9-12).

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