Exercício sobre inequações

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

$\,\dfrac{1}{\,x\,-\,4\,}\;\lt\;\dfrac{2}{\,x\,+\,3\,}\,$

$\,\dfrac{1}{\,x\,-\,1\,}\;\lt\;\dfrac{2}{\,x\,-\,2\,}\,$

$\,\dfrac{x\,+\,1}{\,x\,+\,2\,}\;\gt\;\dfrac{x\,+\,3}{\,x\,+\,4\,}\,$

$\,\dfrac{x\,+\,5}{\,3x\,+\,2\,}\;\leqslant\;\dfrac{x\,-\,2}{\,3x\,+\,5\,}\,$

$\,\dfrac{5x\,+\,2}{\,4x\,-\,1\,}\;\gt\;\dfrac{5x\,-\,1}{\,4x\,+\,5\,}\,$

$\,\dfrac{1}{\,x\,-\,1\,}\; + \;\dfrac{2}{\,x\,-\,2\,}\; - \;\dfrac{3}{\,x\,-\,3\,}\;\lt\;0$

$\,\dfrac{2}{\,3x\,-\,1\,}\; \geqslant \;\dfrac{1}{\,x\,-\,1\,}\; - \;\dfrac{1}{\,x\,+\,1\,}\;$

resposta:

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\; -3\,\lt\,x\,\lt\,4\phantom{X}{\text ou}\phantom{X}x\,\gt\,11\rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;0\,\lt\, x\,\lt\,1\phantom{X}{\text ou}\phantom{X}x\,\gt\,2 \rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-4\,\lt\, x\,\lt\,-2 \rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-\frac{5}{3}$ $\phantom{X}{\text ou}\phantom{X}-\frac{29}{24}\,\leqslant\,x\,\lt\,-\frac{2}{3} \rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{5}{4}\,\lt\,x\,\lt\,-\frac{9}{42}$ $\phantom{X}{\text ou}\phantom{X}x\,\gt\,-\frac{1}{4} \rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,1$ $\phantom{X}{\text ou}\phantom{X}\frac{3}{6}\,\lt\,x\,\lt\,2\phantom{X}{\text ou}\phantom{X}x\,\gt\,3\rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-1\,\lt\,x\,\leqslant\,0$ $\phantom{X}{\text ou}\phantom{X}\frac{1}{3}\,\lt\,x\,\lt\,1\phantom{X}{\text ou}\phantom{X}x\,\geqslant\,3\rbrace\;$