Question

The solution of the inequality $ \frac{1}{2x - 5} > 0 $ is

• A. \( \left[ -\frac{5}{2}, \infty \right) \)
• B. \( \left( \frac{5}{2}, \infty \right) \)
• C. \( \left( -\infty, \frac{5}{2} \right) \)
• D. \( \left( \frac{5}{2}, \infty \right) \)

Hint:

When solving inequalities involving fractions, make sure to pay attention to the signs of both the numerator and denominator.

Answer 1

The Correct Option is B

Step 1: Solve the Inequality
We are given the inequality \( \frac{1}{2x - 5} > 0 \).
For the fraction to be positive, the denominator must be positive (since the numerator is always positive).
So, we solve: \[ 2x - 5 > 0 \quad \Rightarrow \quad x > \frac{5}{2} \] Thus, the solution to the inequality is \( x > \frac{5}{2} \), or \( \left( \frac{5}{2}, \infty \right) \).
Step 2: Conclusion
Thus, the correct solution is \( \left( \frac{5}{2}, \infty \right) \).