Lista de exercícios do ensino médio para impressão
(MACKENZIE-1974) Se o número $\,{\large x}\,$ é solução da equação $\;\sqrt[{\large 3}]{x + 9}\, -\, \sqrt[{\large 3}]{x\, -\, 9}\, =\, 3\;$, então $\;x^{\large 2}\;$ está entre:
a)
0 e 25
b)
25 e 55
c)
55 e 75
d)
75 e 95
e)
95 e 105

 



resposta: Alternativa D
×
FGV-1974) Resolver a desigualdade
$\phantom{XX}1\,-\,3x\, >\, \sqrt{2\,+\,x^2\,-\,3x}\;$:

a)
$x < \dfrac{3-\sqrt{41}}{16}$
b)
$x < \dfrac{1}{3}$
c)
$x < 1\;\;$ ou $\;\;x > 2$
d)
$\dfrac{1}{3}\leqslant x \leqslant \dfrac{3 + \sqrt{41}}{16}$
e)
$x < \dfrac{3 - \sqrt{41}}{16}\;\;$ ou $\;\; x > \dfrac{3 + \sqrt{41}}{16}$

 



resposta: alternativa A
×
(ITA - 1973) A respeito da equação
$\phantom{XX}{\large 3x^2\,-\,4x\,+\,\sqrt{3x^2\,-\,4x\,-6}\,=\,18}\;$
podemos dizer:
a)
${\large \frac{2\pm\sqrt{70}}{3}}\;$ são raízes
b)
A única raiz é $x=3$
c)
A única raiz é $x=2+\sqrt{10}$
d)
tem 2 raízes reais e 2 imaginárias
e)
nenhuma das anteriores

 



resposta: alternativa E
×
(MACKENZIE - 1976) Todas as raízes da equação $\;{\large 2\sqrt{x}\,+\,2x^{(-\frac{1}{2})}\,=\,5}\;$ estão no intervalo:
a)
$\,[-2,-\dfrac{3}{1}]$
b)
$\,[-\dfrac{1}{2}, 1]$
c)
$\,[\dfrac{1}{5},\dfrac{9}{2}]$
d)
$\,[\dfrac{5}{4},7]$
e)
$\,[5,8]$

 



resposta: Alternativa C
×
(FEI-1968) Seja V o conjunto dos números reais que são solução da equação irracional $\; \sqrt{2x} - \sqrt{7 + x} = 1\;$
a) $V = \{2,18\}$
b) $V=\{2\}$
c) $V=\{18\}$
d) $V=\varnothing$
e) nenhuma das anteriores

 



resposta: alternativa C
×
Resolver em $\,\mathbb{R}\,$ as inequações, aplicando as propriedades da desigualdade.
a)
$\,3x\,-\,6\,<\,0\,$
b)
$\,-3x\,+\,6\,<\,0\,$
c)
$\,6\,-\,2x\,\geqslant\,0\,$
d)
$\,x\,-\,3\,<\,x\,+\,3\,$
e)
$\,-x\,+3\,\leqslant \,x\,+\,3\,$
f)
$\,x\,-\,2\, > \,x\,+\,2\,$

 



resposta: Resolução:
a)
$\,3x\,-\,6\,<\,0\;\Rightarrow $ $ \; 3x\,<\,6\; \Rightarrow $ $ \;\boxed{x<2}\,$
b)
$\,-3x\,+\,6\, < \, 0 \; \Rightarrow $ $ \; -3x\, < \, -6 \;\Rightarrow $ $ \; \boxed{x > 2} \,$
c)
$\,6\,-\,2x\,\geqslant 0 \; \Rightarrow $ $ \; -2x\, \geqslant \,-6 \;\Rightarrow $ $ \boxed{x \leqslant 3}\,$
d)
$\,x\,-\,3\, < \, x\,+\,3 \; \Rightarrow $ $ \; 0x\, < 6 \;$ que ocorre para $\; \boxed{\,\vee \negthickspace \negthickspace \negthickspace \negthinspace - x \,\in\, \, \mathbb{R} \,}\,$
e)
$\,-x\,+\,3\,\leqslant \,x\,+\,3\; \Rightarrow $ $ \,-2x \, \leqslant \, 0 \Rightarrow $ $ \boxed{x \geqslant 0}\,$
f)
$\,x\,-\,2\, > \, x\,+\,2 \; \Rightarrow $ $ \; 0x \, > \, 4 \; \Rightarrow $ $ \; \boxed{x \notin \mathbb{R}}\;$ ou $ \; \mathbb{S} \,=\, \varnothing \,$

×
(UFGO - 1982) Se possível, determine em $\,\mathbb{R}\,$ o conjunto solução da inequação $\,(x^2\,-\,2x\,-\,15)\centerdot (-x^2\,-\,2)\centerdot (1\,-\,x^2)\, \leqslant\,0$

 



resposta: $\,V\,=\,\lbrace x\,\in\,\mathbb{R} \mid \,-3\,\leqslant \,x\, \leqslant \,-1\;\text{ou} \;1\,\leqslant \,x\, \leqslant \,5\; \rbrace\,$
×
(ITA - 1990) Considere a região do plano cartesiano x0y definida pelas desigualdades $\,x\,-\,y\,\leqslant\,1\;\mbox{, }\; x\,+\,y\,\geqslant\,1\;$ e $\;(x\,-\,1)^2\,+\,y^2\,\leqslant\,2\,$. O volume do sólido gerado pela rotação desta região em torno do eixo $\,x\,$ é igual a:
a)
$\,\dfrac{4}{3}\pi\,$
b)
$\,\dfrac{8}{3}\pi\,$
c)
$\,\dfrac{4}{3}(2\,-\,\sqrt{2})\pi\,$
d)
$\,\dfrac{8}{3}(\sqrt{2}\,-\,1)\pi\,$
e)
n.d.a.

 



resposta: (B)
×
(FUVEST - 1977) Resolva (em $\,\mathbb{R}\,$) a inequação
$\phantom{XXX}\dfrac{\large x^2\,-\,x\,-\,1}{\large \sqrt{x^2\,-\,3x}}\,\geqslant\,0\phantom{X}$

 



resposta:
$\phantom{X}\dfrac{\large x^2\,-\,x\,-\,1}{\large \sqrt{x^2\,-\,3x}}\,>\,0\phantom{X}\Longleftrightarrow\;\left\{ \begin{array}{rcr} x^{\large 2}\,-\,3x\,>\,0\phantom{XX}&(I) \\ x^{\large 2}\,-\,x\,-\,1\,\geqslant\,0\,&(II) \\ \end{array}\right.$

Solução de (I)
$\,x^2\,-\,3x\,>\,0\;\Rightarrow\;x(x\,-\,3)\,>\,0\;\Longleftrightarrow\;x\,<\,0\,$ ou $\,x\,>\,3\,$
O gráfico de $\;f(x)\,=\,x^2\,-\,3x\;$ é uma parábola como na figura:
gráfico inequação do segundo grau
Temos então do gráfico que a solução de (I) é $\;S_1\,=\,\left\{\,x\,\in\,\mathbb{R}\;|\;x\,<\,0\;\mbox{ou}\;x\,>\,3\,\right\}\,$

Solução de (II)
Como o gráfico $\,f(x)\,=\,x^2\,-\,x\,-\,1\,$ é uma parábola do tipo:
outro gráfico inequação do segundo grau

então: $\,x^2\,-\,x\,-1\,\geqslant\,0\;\Longleftrightarrow\;x\,\leqslant\,\dfrac{1\,-\,\sqrt{5}}{2}\;\mbox{ou}\;x\,\geqslant\,\dfrac{1\,+\,\sqrt{5}}{2}\;\,$ e temos o conjunto temporário da situação (II)
$\;S_2\,=\,\left\{\,x\,\in\,\mathbb{R}\;|\;x\,\leqslant\,\dfrac{1\,-\,\sqrt{5}}{2}\;\mbox{ou}\;x\,\geqslant\,\dfrac{1\,+\,\sqrt{5}}{2}\,\right\}\;$

Solução da questão (Conjunto Verdade)
A solução é o conjunto Verdade, a intersecção dos dois conjuntos $\,S_1\,$ e $\,S_2\,$
$\;V\,=\,S_1\,\cap\,S_2\,=\,\left\{\,x\,\in\,\mathbb{R}\;|\;x\,\leqslant\,\dfrac{1\,-\,\sqrt{5}}{2}\;\mbox{ou}\;x\,>\,3\,\right\}\;$ conforme o diagrama abaixo:
diagrama de eixos inequação
RESPOSTA:
$\,V\,=\,\lbrace\,x\,\in\,\mathbb{R}\,|\,x\,\leqslant\,\dfrac{1\,-\,\sqrt{5}}{2}\;\mbox{ou}\;x\,>\,3 \rbrace\,$

×
(FUVEST - 1977) Construa o gráfico da relação definida pelas desigualdades:

$\phantom{XXX} \left\{\begin{array}{rcr} log_2(y\,-\,x^2)\,\geqslant & log_218\,-\,2\,log_23 \\ \left(\dfrac{1}{2}\right)^{\large 3x\,-\,y}\,\leqslant\,1 & \\ \end{array} \right.$

 



resposta:
gráfico cartesiano das inequações

×
Resolver, em $\,\mathbb{R}\,$, a inequação $\phantom{X}(0,8)^{{}^{\LARGE 4x^{\large 2}\,-\,x}}\,\geqslant\,(0,8)^{{}^{\LARGE 3(x\,+\,1)}}\phantom{X}$

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,\mathbb{R}\;:\;-\frac{1}{2}\,\leqslant\,x\,\leqslant\,\frac{3}{2}\,\rbrace\;$ ou $\;\mathbb{S}\; =\; [-\frac{1}{2}\,;\,\frac{3}{2}]\,$
×
Resolver, em $\,\mathbb{R}\,$, a inequação $\phantom{X}3^{{}^{\Large 2x\,+\,2}}\,\lt\,9^{{}^{\Large 2x\,-\,3}}\phantom{X}$

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,\mathbb{R}\;:\;x\,\gt\,4\,\rbrace\;$ ou $\;\mathbb{S}\; =\; ]4;+\infty[\,$
×
Resolver a inequação $\phantom{X}log{{}_{\Large 7\,}}x\;\geqslant\;log_{{}_{\Large 7\,}}3\;+\;\dfrac{1}{\;2\;}log{{}_{\Large 7\,}}(x\,-\,2)\phantom{X}$

 



resposta: $\,S\,=\,\lbrace\,x\,\in\,\mathbb{R}\;|\;2\,\lt\,x\,\leqslant\,3\;{\text ou}\;x\,\geqslant\,6\rbrace\,$
×
(LONDRINA) Resolver a inequação $\phantom{X}log_{{}_{\Large 2}}(x^2\,-\,1)\;\lt\;3\phantom{X}$

 



resposta: $\,S\,=\,\lbrace\,x\,\in\,\mathbb{R}\;|\;-3\,\lt\,x\,\lt\,-1\;{\text ou}\;1\,\lt\,x\,\lt\,3\,\rbrace\,$
×
Resolver a inequação $\phantom{X}log_{{}_{\LARGE \,(x^2\,-\,4)}}4\;\lt\;log_{{}_{\LARGE \,(x^2\,-\,4)}}5\phantom{X}$

 



resposta: $\,\mathbb{V}\,=\,\lbrace x\,\in\,\mathbb{R}\,|\,x\,\lt\,-\sqrt{5}\;{\text ou}\; \sqrt{5}\,\lt\,x\rbrace\,$
×
Resolver a inequação $\phantom{X}log_{{}_{\LARGE(x\,-\,3)}}{\pi}\;\gt\;log_{{}_{\LARGE(x\,-\,3)}}4\phantom{X}$

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,\mathbb{R}\,|\,3\,\lt\,x\,\lt\,4\rbrace\,$
×
Resolver a inequação $\phantom{X}log_{{}_{\Large 2}}({2^{{}^{\LARGE x\,+\,1}}\,-\,2)}\;\lt\;x\phantom{X}$

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,\mathbb{R}\,|\,0\,\lt\,x\,\lt\,1\rbrace\,$
×
Resolver a inequação $\phantom{X}log_{{}_{\Large (x\,-\,2)}}(x\,-\,1)\;\gt\;0\phantom{X}$.

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,\mathbb{R}\,|\;x\,\gt\,3\rbrace\,$
×
Resolver a inequação $\phantom{X}log_{\,{}_{\LARGE 7}\,}(x^2\,-\,3x)\,\leqslant\,log_{\,{}_{\LARGE 7}\,}18\phantom{X}$

 



resposta: $\,\mathbb{V}\;=\;\lbrace x\,\in\,\mathbb{R}\;|\;-3\,\leqslant\,x\,\leqslant\,0\;{\text ou}\;3\,\leqslant\,x\,\leqslant\,6\rbrace\,$
×
Resolver a inequação $\phantom{X}log_{\,{}_{\LARGE \frac{1}{3}}\,}(x^2\,-\,4x\,+\,3)\,\gt\,-1\phantom{X}$

 



resposta: $\,\mathbb{V}\;=\;\lbrace x\,\in\,\mathbb{R}\;|\;0\,\lt\,x\,\lt\,1\phantom{X}{\text ou}\phantom{X} 3\,\lt\,x\,\lt\,4\rbrace\,$
×
Resolver em $\;{\rm I\!R}\;$ a inequação $\phantom{X}-2\;\lt\;3x\,-\,1\;\lt\;4\phantom{X}$

 



resposta: $\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\dfrac{1}{\;3\;}\,\lt\,x\,\lt\,\dfrac{5}{\;3\;} \rbrace\,$
×
Resolver a inequação $\phantom{X}(3x\,-\,2)(x\,+\,1)(3\,-\,x)\;\lt\;0\phantom{X}$ em $\,{\rm I\!R}\,$

 



resposta: $\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-1\,\lt\,x\,\lt\,\frac{\,2\,}{3}\;{\text ou}\;x\,\gt\,3 \rbrace\,$
×
Resolver em $\,{\rm I\!R}\,$ as inequações:
a)
$\,(3x\,+\,3)(5x\,-\,3)\;\gt\;0\,$
b)
$\,(4\,-\,2x)(5\,+\,2x)\;\lt\;0\,$
c)
$\,(5x\,+\,2)(2\,-\,x)(4x\,+\,3)\;\gt\;0\,$
d)
$\,(3x\,+\,2)(-3x\,+\,4)(x\,-\,6)\;\lt\;0\,$
e)
$\,(6x\,-\,1)(2x\,+\,7)\;\geqslant\;0\,$

 



resposta:
a)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-1\;{\text ou}\;x\,\gt\,\frac{\,3\,}{5} \rbrace\,$
b)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-\frac{\,5\,}{2}\;{\text ou}\;x\,\gt\,2 \rbrace\,$
c)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-\frac{\,3\,}{4}\;{\text ou}\;-\frac{\,2\,}{5}\,\lt\,x\,\lt\,2 \rbrace\,$
d)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{\,2\,}{3}\,\lt\,x\,\lt\,\frac{\,4\,}{3}\;{\text ou}\;x\,\gt\,6 \rbrace\,$
e)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{\,7\,}{2}\;{\text ou}\;x\,\geqslant\,\frac{\,1\,}{6} \rbrace\,$

×
Resolver em $\,{\rm I\!R}\,$ as inequações:
a)
$\,(5\,-\,2x)(-7x\,-\,2)\;\leqslant\;0\,$
b)
$\,(3\,-\,2x)(4x\,+\,1)(5x\,+\,3)\;\geqslant\;0\,$
c)
$\,(5\,-\,3x)(7\,-\,2x)(1\,-\,4x)\;\leqslant\;0\,$

 



resposta:
a)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{\,2\,}{7}\,\leqslant\,x\,\leqslant\,\frac{\,5\,}{2} \rbrace\,$
b)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{\,3\,}{5}\;{\text ou}\;-\frac{\,1\,}{4}\leqslant\,x\,\leqslant\,\frac{3}{\,2\,} \rbrace\,$
c)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;\frac{\,1\,}{4}\leqslant\,x\,\leqslant\,\frac{\,5\,}{3}\;{\text ou}\;x\,\geqslant\,\frac{\,7\,}{2} \rbrace\,$

×
Resolver em $\,{\rm I\!R}\,$ as inequações:
a)
$\,(x\,-\,3)^{{}^{\LARGE 4}}\;\gt\;0\,$
b)
$\,(3\,+\,8)^{{}^{\LARGE 3}}\;\lt\;0\,$
c)
$\,(4\,-\,5x)^{{}^{\LARGE 6}}\;\lt\;0\,$
d)
$\,(1\,-\,7x)^{{}^{\LARGE 5}}\;\gt\;0\,$
e)
$\,(3x\,+\,5)^{{}^{\LARGE 2}}\;\geqslant\;0\,$
f)
$\,(5x\,+\,1)^{{}^{\LARGE 3}}\;\leqslant\;0\,$
g)
$\,(4\,+\,3x)^{{}^{\LARGE 4}}\;\leqslant\;0\,$
h)
$\,(3x\,-\,8)^{{}^{\LARGE 5}}\;\geqslant\;0\,$

 



resposta:
a)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\ne\,3\rbrace\;$
b)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-\frac{\,8\,}{3}\rbrace\;$
c)
$\,\mathbb{S}\;=\;\varnothing\;$
d)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,\frac{\,1\,}{7}\rbrace\;$
e)
$\,\mathbb{S}\;=\;{\rm I\!R}\;$
f)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{\,1\,}{5}\rbrace\;$
g)
$\,\mathbb{S}\;=\;\lbrace -\frac{\,4\,}{3}\rbrace\;$
h)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\geqslant\,\frac{\,8\,}{3}\rbrace\;$

×
Resolver em $\,{\rm I\!R}\,$ a inequação $\phantom{X}(x\,-\,3)^{{}^{\LARGE 5}}\,\centerdot\,(2x\,+\,3)^{{}^{\LARGE 6}}\;\lt\;0\phantom{X}$.

 



resposta: $\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,3\phantom{X}{\text e}\phantom{X}x\,\ne\,-\frac{\,3\,}{2}\rbrace\;$
×
Resolver em $\,{\rm I\!R}\,$ as inequações:
a)
$\phantom{X}(5x\,+\,4)^{{}^{\LARGE 4}}\,\centerdot\,(7x\,-\,2)^{{}^{\LARGE 3}}\;\geqslant\;0\phantom{X}$
b)
$\phantom{X}(3x\,+\,1)^{{}^{\LARGE 3}}\,\centerdot\,(2\,-\,5x)^{{}^{\LARGE 5}}\,\centerdot\,(x\,+\,4)^{{}^{\LARGE 8}}\;\gt\;0\phantom{X}$
c)
$\phantom{X}(x\,+\,6)^{{}^{\LARGE 7}}\,\centerdot\,(6x\,-\,2)^{{}^{\LARGE 4}}\,\centerdot\,(4x\,+\,5)^{{}^{\LARGE 10}}\;\leqslant\;0\phantom{X}$
d)
$\phantom{X}(5x\,-\,1)^{{}^{\LARGE 3}}\,\centerdot\,(2x\,+\,6)^{{}^{\LARGE 8}}\,\centerdot\,(4\,-\,6x)^{{}^{\LARGE 6}}\;\geqslant\;0\phantom{X}$.

 



resposta:
a)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\geqslant\,\frac{\,2\,}{7}\rbrace\;$
b)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{\,1\,}{3}\,\lt\,x\,\lt\,\frac{\,2\,}{5}\rbrace\;$
c)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-6\phantom{X}{\text ou}\phantom{X}x\,=\,\frac{\,1\,}{3}\phantom{X}{\text ou}\phantom{X}x\,=\,-\frac{\,5\,}{4}\rbrace\;$
d)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\geqslant\,\frac{\,1\,}{5}\phantom{X}{\text ou}\phantom{X}x\,=\,-3\rbrace\;$

×
Resolver em $\,{\rm I\!R}\,$ a inequação $\phantom{X}\dfrac{\;3x\,+\,4\;}{1\,-\,x}\phantom{X}$

 



resposta: $\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{2}{5}\phantom{X}{\text e}\phantom{X}x\,\gt\,1\rbrace\;$
×
Resolver as inequações:
a)
$\,4\,\lt\,x^2\,-\,12\,\leqslant\,4x\,$
b)
$\,x^2\,+\,1\,\lt\,2x^2\,-\,3\,\leqslant\,-5x\,$
c)
$\,0\,\leqslant\,x^2\,-\,3x\,+\,2\,\leqslant\,6\,$
d)
$\,7x\,+\,1\,\lt\,x^2\,+\,3x\,-\,4\,\leqslant\,2x\,+\,2\,$
e)
$\,0\,\lt\,x^2\,+\,x\,+\,1\,\lt\,1\,$
e)
$\,4x^2\,-\,5x\,+\,4\,\lt\,3x^2\,-\,6x\,+\,6\,\lt\,x^2\,+\,3x\,-\,4\,$

 



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

×
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)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{\,3\,}{2}\phantom{X}{\text ou}\phantom{X}x\,\gt\,-\frac{\,1\,}{3}\rbrace\;$
×
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)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;1\,\leqslant\,x\,\lt\,2\rbrace\;$
×
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 a inequação $\phantom{X}x^2\,-\,2x\,+\,2\;\gt\;0\phantom{X}$.

 



resposta: $\,\mathbb{S}\,=\,{\rm I\!R}\,$
×
Resolver a inequação $\phantom{X}x^2\,-\,2x\,+\,1\;\leqslant\;0\phantom{X}$.

 



resposta: $\,\mathbb{S}\,=\,\lbrace1\rbrace\,$
×
Resolver a inequação $\phantom{X}-2x^2\,+\,3x\,+\,2\;\geqslant\;0\phantom{X}$.

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{1}{2}\,\leqslant\,x\,\leqslant\,2\rbrace\;$
×
Resolver as inequações do segundo grau a seguir em $\,{\rm I\!R}\,$:
a)
$\,x^2\,-\,3x\,+\,2\;\gt\;0\,$
b)
$\,-x^2\,+\,x\,+\,6\;\gt\;0\,$
c)
$\,-3x^2\,-\,8x\,+\,3\;\leqslant\;0\,$
d)
$\,-x^2\,+\,\dfrac{\,3\,}{\,2\,}x\,+\,10\;\geqslant\;0\,$
e)
$\,8x^2\,-\,14x\,+\,3\;\leqslant\;0\,$
f)
$\,4x^2\,-\,4x\,+\,1\;\gt\;0\,$
g)
$\,x^2\,-\,6x\,+\,9\;\geqslant\;0\,$
h)
$\,-4x^2\,+\,12x\,-\,9\;\geqslant\;0\,$
i)
$\,x^2\,+\,3x\,+\,7\;\gt\;0\,$
j)
$\,-3x^2\,+\,3x\,-\,3\;\lt\;0\,$
k)
$\,2x^2\,-\,4x\,+\,5\;\lt\;0\,$
l)
$\,-\dfrac{\,1\,}{\,3\,}x^2\,+\,\dfrac{\,1\,}{\,2\,}x\,-\,\dfrac{\,1\,}{\,4\,}\;\gt\;0\,$

 



resposta:
a)
$\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,1\phantom{X}{\text ou}\phantom{X}x\,\gt\,2\rbrace\;$
b)
$\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|-2\,\lt\,x\,\lt\,3\rbrace\;$
c)
$\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-3\phantom{X}{\text ou}\phantom{X}x\,\geqslant\,\frac{\,1\,}{\,3\,}\rbrace\;$
d)
$\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{\,5\,}{\,2\,}\,\leqslant\,x\,\leqslant\,4\rbrace\;$
e)
$\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;\frac{\,1\,}{\,4\,}\,\leqslant\,x\,\leqslant\,\frac{\,3\,}{\,2\,}\rbrace\;$
f)
$\,\mathbb{S}\,=\,{\rm I\!R}\;-\;\lbrace \frac{\,1\,}{\,2\,}\rbrace\,$
g)
$\,\mathbb{S}\,=\,{\rm I\!R}\,$
h)
$\,\mathbb{S}\,=\,\lbrace \frac{\,3\,}{\,2\,}\rbrace\;$
i)
$\,\mathbb{S}\,=\,{\rm I\!R}\,$
j)
$\,\mathbb{S}\,=\,{\rm I\!R}\,$
k)
$\,\mathbb{S}\,=\,\varnothing\,$
l)
$\,\mathbb{S}\,=\,\varnothing\,$

×
Resolver a inequação $\phantom{X}(x^2\,-\,x\,-\,2)(-x^2\,+\,4x\,-\,3)\;\lt\;0\phantom{X}$ em $\,{\rm I\!R}\,$.

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;-1\,\lt\,x\,\lt\,1\phantom{X}{\text ou}\phantom{X}2\,\lt\,x\,\lt\,3\rbrace\;$
×
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)
$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-1\,\lt\,x\,\leqslant\,0$ $\phantom{X}{\text ou}\phantom{X}\frac{1}{3}\,\lt\,x\,\lt\,1\phantom{X}{\text ou}\phantom{X}x\,\geqslant\,3\rbrace\;$

×
Resolver em $\,{\rm I\!R}\,$ as inequações:
a)
$\,(1\,-\,4x^2)\centerdot(2x^2\,+\,3)\,\gt\,0\,$
b)
$\,(2x^2\,-\,7x\,+\,6)\centerdot(2x^2\,-\,7x\,+\,5)\,\leqslant\,0\,$
c)
$\,(x^2\,-\,x\,-\,6)\centerdot(-x^2\,+\,2x\,-1)\,\gt\,0\,$
d)
$\,(x^2\,+\,x\,-\,6)\centerdot(-x^2\,-2x\,+\,3)\,\geqslant\,0\,$
e)
$\,x^3\,-\,2x^2\,-\,x\,+\,2\,\gt\,0\,$
f)
$\,2x^3\,-\,6x^2\,+\,x\,-\,3\,\leqslant\,0\,$

 



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

×
(MAPOFEI - 1971) É dada a função $\phantom{X}y\,=\,(2x^2\,-\,9x\,-\,5)(x^2\,-\,2x\,+2)\phantom{X}$
Determinar:
a)
os pontos de intersecção do gráfico da função com o eixo das abscissas.
b)
o conjunto dos valores de x para os quais $\,y\,\leqslant\,0\,$.

 



resposta:
a) P1 = (5, 0) e P2 = (-1/2, 0)
b) $\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{1}{2}\,\leqslant\,x\,\leqslant\,5\rbrace\;$

×
Resolver a inequação $\phantom{X}\dfrac{\;2x^2\,+\,x\,-\,1\;}{2x\,-\,x^2}\;\geqslant\;0\phantom{X}$

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\leqslant\,-1\phantom{X}{\text ou}\phantom{X}0\,\lt\,x\,\leqslant\,\frac{1}{2}\phantom{X}{\text ou}\phantom{X}x\,\gt\,2\rbrace\;$
×
Resolver as inequações em $\,{\rm I\!R}\,$:
a)
$\,\dfrac{\;4x^2\,+\,x\,-\,5\;}{2x^2\,-3x\,-\,2}\;\gt\;0\,$
b)
$\,\dfrac{\;-9x^2\,+\,9x\,-\,2\;}{\;3x^2\,+\,7x\,+\,2\;}\;\geqslant\;0\,$
c)
$\,\dfrac{\;x^2\,+\,2x\;}{\;x^2\,+\,5x\,+\,6\;}\;\geqslant\;0\,$
d)
$\,\dfrac{\;2\,-\,3x\;}{\;2x^2\,+\,3x\,-\,2\;}\;\lt\;0\,$
e)
$\,\dfrac{\;x^2\,+\,3x\,-\,16\;}{\;-x^2\,+\,7x\,-\,10\;}\;\geqslant\;1\,$
f)
$\,\dfrac{\;2x^2\,+\,4x\,+\,5\;}{\;3x^2\,+\,7x\,+\,2\;}\;\lt\;-2\,$
g)
$\,\dfrac{\;6x^2\,+\,12x\,+\,17\;}{\;-2x^2\,+\,7x\,-\,5\;}\;\geqslant\;-1\,$
h)
$\,\dfrac{\;(x\,+\,1)^3\,-\,1\;}{\;(x\,-\,1)^3\,+\,1\;}\;\gt\;1\,$

 



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

×
Resolver os sistemas de inequações:
a)
$\,\left\{\begin{array}{rcr} x^2\,+\,x\,-\,2\;\gt\;0 & \\ 3x\,-\,x^2\,\lt\,0\phantom{XX}& \\ \end{array} \right.\,$ 
b)
$\,\left\{\begin{array}{rcr} x^2\,+\,x\,-\,20\;\leqslant\;0\;\;& \\ x^2\,-\,4x\,-\,21\,\gt\,0\;& \\ \end{array} \right.\,$
c)
$\,\left\{\begin{array}{rcr} 1\,+\,2x\;\geqslant\;0\phantom{XXXX}& \\ -4x^2\,+\,8x\,-\,3\,\lt\,0\;& \\ \end{array} \right.\,$
d)
$\,\left\{\begin{array}{rcr} -2x^2\,-\,x\,+\,1\,\geqslant\,0\phantom{X}& \\ 4x^2\,-\,8x\,+\,3\;\leqslant\,0\phantom{X}& \\ \end{array} \right.\,$

 



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)$\,\mathbb{S}\,=\,\lbrace \frac{1}{2}\rbrace$

×
Resolver a inequação $\phantom{X}x^4\,-\,5x^2\,+\,4\,\geqslant\,0\phantom{X}$ em $\,{\rm I\!R}\,$.

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-2\,\phantom{X}{\text ou}\phantom{X}-1\,\leqslant\,x\,\leqslant\,1\phantom{X}{\text ou}\phantom{X}x\,\geqslant\,2\rbrace$

×
Resolver em $\,{\rm I\!R}\,$ as inequações a seguir:
a)
$\,x^4\,-\,10x^2\,+\,9\,\leqslant\,0\,$
b)
$\,x^4\,-\,3x^2\,-\,9\,\gt\,0\,$
c)
$\,x^4\,+\,8x^2\,-\,9\,\lt\,0\phantom{X}$
d)
$\,2x^4\,-\,3x^2\,+\,4\,\lt\,0\,$
e)
$\,x^6\,-\,7x^3\,-\,8\,\geqslant\,0\phantom{X}$
f)
$\,3x^4\,-\,5x^2\,+\,4\,\gt\,0\,$

 



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

×
O conjunto verdade da inequação $\phantom{X}|x\,-\,3|\,+\,|x|\,\geqslant\,0\phantom{X}$ é:
a)
$\,\varnothing\phantom{\lbrace x\,\in\,{\rm I\!R}\,|\,x\gt\,3\rbrace}$
b)
$\,{\rm I\!R}\,$
c)
$\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\gt\,3\rbrace\,$
d)
$\,\lbrace x\,\in\,{\rm I\!R}\;|\;0\,\lt\,x\,\lt\,3\rbrace\,$
e)
$\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\geqslant\,0\rbrace\,$
 
 

 



resposta: (B)
×
O conjunto verdade da inequação $\phantom{X}|x\,-\,3|\,+\,|x\,-\,1|\,\geqslant\,4\phantom{X}$ é:
a)
$\,\varnothing\phantom{\lbrace x\,\in\,{\rm I\!R}\;|x\,\leqslant\,0\phantom{X}{\text ou}\phantom{X}x\,\geqslant\,4\rbrace}$
b)
$\,{\rm I\!R}\,$
c)
$\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,0\phantom{X}{\text ou}\phantom{X}x\,\geqslant\,4\rbrace\,$
d)
$\,\lbrace x\,\in\,{\rm I\!R}\;|\;0\,\leqslant\,x\,\leqslant\,4\rbrace\,$
e)
$\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\geqslant\,1\rbrace\,$
 
 

 



resposta: (C)
×
Resolver em $\;{\rm I\!R}\;$ a inequação $\phantom{X}|x\,-\,3|\,\gt\,7\phantom{X}$

 



resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-4\phantom{X}{\text ou}\phantom{X}10\,\lt\,x\rbrace\,$
×
(FATEC - 1983) O conjunto solução da inequação $\phantom{X}|\,2x\,-\,3\,|\;\leqslant\;0,002\phantom{X}$ em $\;{\rm I\!R} \;$, é:
a)
$\,{\rm I\!R} \phantom{XXXXXXX}$
b)
$\,]-\infty\,;\,1,51]\,$
c)
$\,[-1,51\,;\,-1,49]\,$
d)
$\,[1,49\,;\,1,51]\,$
e)
$\,[5,96;\,6,04]\,$
 
 

 



resposta: (D)
×
(FUVEST - 1998)
a) Expresse $\phantom{X}\operatorname{sen}3\,\alpha\phantom{X}$ em função de $\phantom{X}\operatorname{sen}\alpha\,$.
b) Resolva a inequação $\phantom{X}\operatorname{sen}3\,\alpha\;\gt\;2\operatorname{sen}\alpha\phantom{X}\,$ para $\phantom{X}0\,\lt\,\alpha\,\lt\,\pi\;$.

 



resposta: a) sen3α = 3.senα - 4.sen³α
b)$\,S\,=\,$ $\lbrace\,\alpha\,\in\,{\rm\,I\!R}\,|\,0\,\lt\,\alpha\,\lt\,\frac{\,\pi\,}{\,6\,}\;{\text ou}\;\frac{\,5\pi\,}{\,6\,}\,\lt\,\alpha\,\lt\,\pi\,\rbrace\,$
×
Veja exercÍcio sobre:
inequação
inequação do segundo grau