Question

The set of admissible values of $x$ such that $\frac{2x+3}{2x-9}<0$ is

• A. $\left(-\infty ,-\frac{3}{2}\right)\cup \left(\frac{9}{2},\infty \right)$
• B. $(-\infty ,0)\cup \left(\frac{9}{2},\infty \right)$
• C. $\left(-\frac{3}{2},0\right)$
• D. $\left(0,\frac{9}{2}\right)$
• E. $\left(-\frac{3}{2},\frac{9}{2}\right)$

Answer 1

Answer: (E)

Given, $\frac{2x+3}{2x-9}<0$
$\Rightarrow$ $2x+3<0$ and $2y-9>0$ or $2x+3>0$ and $2x-9<0$ and $x\ne \frac{9}{2}$
$\Rightarrow$ $x<-\frac{3}{2}$ and $x>\frac{9}{2}$ or $x>-\frac{3}{2}$ and $x<\frac{9}{2}$ and $x\ne \frac{9}{2}$
$\Rightarrow$ $\left(-\frac{3}{2},\frac{9}{2}\right)$