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Question
\[\frac{4x + 3}{2x - 5} < 6\]
Solution
\[\frac{4x + 3}{2x - 5} < 6\]
\[ \Rightarrow \frac{4x + 3}{2x - 5} - 6 < 0\]
\[ \Rightarrow \frac{4x + 3 - 6\left( 2x - 5 \right)}{2x - 5} < 0\]
\[ \Rightarrow \frac{4x + 3 - 12x + 30}{2x - 5} < 0\]
\[ \Rightarrow \frac{- 8x + 33}{2x - 5} < 0\]
\[ \Rightarrow \frac{8x - 33}{2x - 5} > 0\]
\[x \in \left( - \infty , \frac{5}{2} \right) \cup \left( \frac{33}{8}, \infty \right)\]
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