CUET · MATHS · PYQ PAPER 2025
Solution of the inequality \(\frac{2 x+3}{4 x-5} \geq 0\) is
- A \(\left(-\frac{3}{2}, \frac{5}{4}\right)\)
- B \(\left(-\infty,-\frac{3}{2}\right] \cup\left[\frac{5}{4}, \infty\right)\)
- C \(\left[-\frac{3}{2}, \frac{5}{4}\right)\)
- D \(\left(-\infty,-\frac{3}{2}\right] \cup\left(\frac{5}{4}, \infty\right)\)
Answer & Solution
Correct Answer
(D) \(\left(-\infty,-\frac{3}{2}\right] \cup\left(\frac{5}{4}, \infty\right)\)
Step-by-step Solution
Detailed explanation
\(2x+3=0 \Rightarrow x=-\frac{3}{2}\) \(4x-5=0 \Rightarrow x=\frac{5}{4}\) For \(\frac{2x+3}{4x-5} \geq 0\): If \(x \leq -\frac{3}{2}\), numerator is \(\leq 0\), denominator is \(If \(-\frac{3}{2} 0\), denominator is \(If \(x > \frac{5}{4}\), numerator is…
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