Exercício sobre inequação do segundo grau II

Resolver os sistemas de inequações:

$\,\left\{\begin{array}{rcr} x^2\,+\,x\,-\,2\;\gt\;0 & \\ 3x\,-\,x^2\,\lt\,0\phantom{XX}& \\ \end{array} \right.\,$

$\,\left\{\begin{array}{rcr} x^2\,+\,x\,-\,20\;\leqslant\;0\;\;& \\ x^2\,-\,4x\,-\,21\,\gt\,0\;& \\ \end{array} \right.\,$

$\,\left\{\begin{array}{rcr} 1\,+\,2x\;\geqslant\;0\phantom{XXXX}& \\ -4x^2\,+\,8x\,-\,3\,\lt\,0\;& \\ \end{array} \right.\,$

$\,\left\{\begin{array}{rcr} -2x^2\,-\,x\,+\,1\,\geqslant\,0\phantom{X}& \\ 4x^2\,-\,8x\,+\,3\;\leqslant\,0\phantom{X}& \\ \end{array} \right.\,$

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

×