Inequalities

Step 1: Understanding the Problem
We are given that , and we need to check which of the options is true.
Step 2: Analyzing the Options
Option (a) is incorrect because is always greater than for .
Option (b) is incorrect because is less than for .
Option (c) is correct because the product is negative when because one term is positive and the other is negative.
Option (d) is incorrect because the fraction is negative for .
Step 3: Conclusion
Thus, the correct option is .

Step 1: Solve the Inequality
We are given the inequality .
For the fraction to be positive, the denominator must be positive (since the numerator is always positive).
So, we solve: Thus, the solution to the inequality is , or .
Step 2: Conclusion
Thus, the correct solution is .