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Mathematics: Inequalities

### Solution

**contradiction**for this case. \[\] If \(x\geq0\) \[\frac{x+1+2 x-4}{x-2}<0\] \[\frac{3x-3}{x-2}<0\] \[\frac{(3x-3)(x-2)}{(x-2)^{2}}<0\] \[\frac{3(x-1)(x-2)}{(x-2)^{2}}<0\] \[\Rightarrow 1<x<2\] For this case we have solutions. \[\] Finally, \[\huge S_{\mathbb{R}}=[0,+\infty[\cap] 1,2[=] 1,2[\]

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