Exercício sobre inequações simultâneas

Resolver os sistemas de inequações em $\phantom{X}{\rm I\!R}\phantom{X}$:

$\,\left\{\begin{array}{rcr} 3x\,-\,2\,\gt\,4x\,+\,1\;& \\ 5x\,+\,1\,\leqslant\,2x\,-\,5\;& \\ \end{array} \right.\,$

$\,\left\{\begin{array}{rcr} 5\,-\,2x\;\lt\;0\phantom{XXX}& \\ 3x\,+\,1\,\geqslant\,4x\,-\,5\;& \\x\,-\,3\,\geqslant\,0\phantom{XXXX}& \\ \end{array} \right.\,$

$\,\left\{\begin{array}{rcr} 3x\,+\,2\,\geqslant\,5x\,-\,2\;& \\ 4x\,-\,1\,\gt\,3x\,-\,4\;& \\3\,-\,2x\,\lt\,x\,-\,6\phantom{X}& \\ \end{array} \right.\,$

$\,\left\{\begin{array}{rcr}\dfrac{\;2x\,-\,5\;}{\;1\,-\,x\;} \;\leqslant\;-2\phantom{X}& \\ \dfrac{\,x^2\,+\,x\,+\,3\,}{x\,+\,1}\,\gt\,x\;& \\ \end{array} \right.\,$

resposta:

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-3\,\rbrace\,$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;3\,\leqslant\,x\,\leqslant\,6 \rbrace\,$

$\,\mathbb{S}\;=\;\varnothing\,$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-1\,\lt\,x\,\lt\,1 \rbrace\,$