Exercício sobre inequações

Resolver as inequações em $\,{\rm I\!R}\,$:

$\,\dfrac{\;(1\,-\,2x)(3\,+\,4x)\;}{(4\,-\,x)}\;\gt\;0\,$

$\,\dfrac{\;(3x\,+\,1)\;}{\;(2x\,+\,5)(5x\,+\,3)\;}\;\lt\;0\,$

$\,\dfrac{\;(5x\,+\,4)(4x\,+\,1)\;}{(5\,-\,4x)}\;\geqslant\;0\,$

$\,\dfrac{\;(1\,-\,2x)\;}{\;(5\,-\,x)(3\,-\,x)\;}\;\leqslant\;0\,$

resposta: a)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;\frac{-3}{4}\,\lt\,x\,\lt\,\frac{1}{2}\phantom{X}{\text ou}\phantom{X}x\,\gt\,4\rbrace\;$ b)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-\frac{5}{2}\phantom{X}{\text ou}\phantom{X}-\frac{3}{5}\,\lt\,x\,\lt\,-\frac{1}{3}\rbrace\;$ c)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{4}{5}\phantom{X}{\text ou}\phantom{X}-\frac{1}{4}\,\leqslant\,x\,\lt\,\frac{5}{4}\rbrace\;$ d)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;\frac{1}{2}\,\leqslant\,x\,\lt\,3\phantom{X}{\text ou}\phantom{X}x\,\gt\,5\rbrace\;$
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