Solve the following

Question:

$\frac{4 x+3}{2 x-5}<6$

Solution:

$\frac{4 x+3}{2 x-5}<6$

$\Rightarrow \frac{4 x+3}{2 x-5}-6<0$

$\Rightarrow \frac{4 x+3-6(2 x-5)}{2 x-5}<0$

$\Rightarrow \frac{4 x+3-12 x+30}{2 x-5}<0$

$\Rightarrow \frac{-8 x+33}{2 x-5}<0$

$\Rightarrow \frac{8 x-33}{2 x-5}>0$

$x \in\left(-\infty, \frac{5}{2}\right) \cup\left(\frac{33}{8}, \infty\right)$

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