Lista de exercícios do ensino médio para impressão
Resolver em $\,{\rm I\!R}\,$ a inequação $\phantom{X}\dfrac{\;3x\,+\,4\;}{1\,-\,x}\phantom{X}$

resposta: $\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{2}{5}\phantom{X}{\text e}\phantom{X}x\,\gt\,1\rbrace\;$
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Resolver em $\,{\rm I\!R}\,$ as inequaçoes abaixo
a)
$\,\dfrac{\;2x\,+\,1\;}{\;x\,+\,2\;}\;\gt\;0\,$
b)
$\,\dfrac{\;3x\,-\,2\;}{\;3\,-\,2x\;}\;\lt\;0\,$
c)
$\,\dfrac{\;3\,-\,4x\;}{\;5x\,+\,1\;}\;\geqslant\;0\,$
d)
$\,\dfrac{\;-3\,-\,2x\;}{\;3x\,+\,1\;}\;\leqslant\;0\,$

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

resposta: a)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,\frac{\,7\,}{8}\phantom{X}{\text ou}\phantom{X}x\,\gt\,\frac{\,4\,}{3}\rbrace\;$ b)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-10\phantom{X}{\text ou}\phantom{X}x\,\gt\,\frac{\,-4\,}{3}\rbrace\;$ c)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-2\,\leqslant\,x\,\lt\,-1\rbrace\;$ d)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;1\,\leqslant\,x\,\lt\,2\rbrace\;$
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Resolver as inequações em $\,{\rm I\!R}\,$:
a)
$\,\dfrac{\;(1\,-\,2x)(3\,+\,4x)\;}{(4\,-\,x)}\;\gt\;0\,$
b)
$\,\dfrac{\;(3x\,+\,1)\;}{\;(2x\,+\,5)(5x\,+\,3)\;}\;\lt\;0\,$
c)
$\,\dfrac{\;(5x\,+\,4)(4x\,+\,1)\;}{(5\,-\,4x)}\;\geqslant\;0\,$
d)
$\,\dfrac{\;(1\,-\,2x)\;}{\;(5\,-\,x)(3\,-\,x)\;}\;\leqslant\;0\,$

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)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;\frac{1}{2}\,\leqslant\,x\,\lt\,3\phantom{X}{\text ou}\phantom{X}x\,\gt\,5\rbrace\;$
×
Resolver as inequações em $\,{\rm I\!R}\,$:
a)
$\,\dfrac{1}{\,x\,-\,4\,}\;\lt\;\dfrac{2}{\,x\,+\,3\,}\,$
b)
$\,\dfrac{1}{\,x\,-\,1\,}\;\lt\;\dfrac{2}{\,x\,-\,2\,}\,$
c)
$\,\dfrac{x\,+\,1}{\,x\,+\,2\,}\;\gt\;\dfrac{x\,+\,3}{\,x\,+\,4\,}\,$
d)
$\,\dfrac{x\,+\,5}{\,3x\,+\,2\,}\;\leqslant\;\dfrac{x\,-\,2}{\,3x\,+\,5\,}\,$
e)
$\,\dfrac{5x\,+\,2}{\,4x\,-\,1\,}\;\gt\;\dfrac{5x\,-\,1}{\,4x\,+\,5\,}\,$
f)
$\,\dfrac{1}{\,x\,-\,1\,}\; + \;\dfrac{2}{\,x\,-\,2\,}\; - \;\dfrac{3}{\,x\,-\,3\,}\;\lt\;0$
g)
$\,\dfrac{2}{\,3x\,-\,1\,}\; \geqslant \;\dfrac{1}{\,x\,-\,1\,}\; - \;\dfrac{1}{\,x\,+\,1\,}\;$

resposta:
a)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\; -3\,\lt\,x\,\lt\,4\phantom{X}{\text ou}\phantom{X}x\,\gt\,11\rbrace\;$
b)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;0\,\lt\, x\,\lt\,1\phantom{X}{\text ou}\phantom{X}x\,\gt\,2 \rbrace\;$
c)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-4\,\lt\, x\,\lt\,-2 \rbrace\;$
d)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-\frac{5}{3}$ $\phantom{X}{\text ou}\phantom{X}-\frac{29}{24}\,\leqslant\,x\,\lt\,-\frac{2}{3} \rbrace\;$
e)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{5}{4}\,\lt\,x\,\lt\,-\frac{9}{42}$ $\phantom{X}{\text ou}\phantom{X}x\,\gt\,-\frac{1}{4} \rbrace\;$
f)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,1$ $\phantom{X}{\text ou}\phantom{X}\frac{3}{6}\,\lt\,x\,\lt\,2\phantom{X}{\text ou}\phantom{X}x\,\gt\,3\rbrace\;$
c)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-1\,\lt\,x\,\leqslant\,0$ $\phantom{X}{\text ou}\phantom{X}\frac{1}{3}\,\lt\,x\,\lt\,1\phantom{X}{\text ou}\phantom{X}x\,\geqslant\,3\rbrace\;$

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Veja exercÍcio sobre:
inequações
inequação quociente