Question
Solve the following linear inequations in R: $\frac{5\text{x}+8}{4-\text{x}}<2$

Answer

$\frac{5\text{x}+8}{4-\text{x}}<2$ $\frac{5\text{x}+8}{4-\text{x}}-2<0$ $\frac{5\text{x}+8-2(4-\text {x})}{4-\text{x}}<0$ $\frac{5\text{x}+8-8+2\text{x}}{4-\text{x}}<0$ $\frac{7\text{x}}{4-\text{x}}<0$ Case 1: $7\text{x}>0$ and $4-\text{x}<0$ $\Rightarrow\text{x}>0$ and $4<\text{x}$ $\Rightarrow\text{x}<0$ Hence solution set is $(-\infty,0)\cup(4,\infty)$

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