Solve the following linear inequations in R: 2x-3 3x-7 >0 - Vidyadip

Question

Solve the following linear inequations in R: $\frac{2\text{x}-3}{3\text{x}-7}>0$

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Answer

$\frac{2\text{x}-3}{3\text{x}-7}>0$ Case 1: 2x - 3 > 0 and 3x - 7 > 0 $\Rightarrow\text{x}>\frac{3}{2}$ and $\text{x}<\frac{7}{3}$ $\Rightarrow\text{x}>\frac{7}{3}$ Case 2: 2x - 3 < 0 and 3x - 1 < 0 $\Rightarrow\text{x}<\frac{3}{2}$ and $\text{x}<\frac{7}{3}$ $\Rightarrow\text{x}<\frac{3}{2}$ $\therefore$ $\Big(-\infty,\frac{3}{2}\Big)\cup\Big(\frac{7}{3},\infty\Big)$Solution set

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