Exercício sobre inequações

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

$\phantom{X}(5x\,+\,4)^{{}^{\LARGE 4}}\,\centerdot\,(7x\,-\,2)^{{}^{\LARGE 3}}\;\geqslant\;0\phantom{X}$

$\phantom{X}(3x\,+\,1)^{{}^{\LARGE 3}}\,\centerdot\,(2\,-\,5x)^{{}^{\LARGE 5}}\,\centerdot\,(x\,+\,4)^{{}^{\LARGE 8}}\;\gt\;0\phantom{X}$

$\phantom{X}(x\,+\,6)^{{}^{\LARGE 7}}\,\centerdot\,(6x\,-\,2)^{{}^{\LARGE 4}}\,\centerdot\,(4x\,+\,5)^{{}^{\LARGE 10}}\;\leqslant\;0\phantom{X}$

$\phantom{X}(5x\,-\,1)^{{}^{\LARGE 3}}\,\centerdot\,(2x\,+\,6)^{{}^{\LARGE 8}}\,\centerdot\,(4\,-\,6x)^{{}^{\LARGE 6}}\;\geqslant\;0\phantom{X}$.

resposta:

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\geqslant\,\frac{\,2\,}{7}\rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{\,1\,}{3}\,\lt\,x\,\lt\,\frac{\,2\,}{5}\rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-6\phantom{X}{\text ou}\phantom{X}x\,=\,\frac{\,1\,}{3}\phantom{X}{\text ou}\phantom{X}x\,=\,-\frac{\,5\,}{4}\rbrace\;$

$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\geqslant\,\frac{\,1\,}{5}\phantom{X}{\text ou}\phantom{X}x\,=\,-3\rbrace\;$