% inéquations
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%%%     créée le Tue, 09 Sep 2008 09:43:59 +0200                 %%%
%%%     sur http://allken-bernard.org/pierre/phpmyexercices      %%%
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% Apparence des exercices
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\rhead{\textbf{\thepage/\pageref{fin}}}
\lfoot{\small \textit{Lycée Joachim du Bellay}}
\cfoot{\small \textit{Mathématiques, prépa ECE1}}
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%%%     Exercice 52
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[4(x-2)-x<7(2x+1)\]
\end{exercice}


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%%%     Exercice 54
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{x-3}{2}-\frac{3x-4}{3}-\frac{1}{4}>\frac{1}{6}+\frac{2-x}{12}\]
\end{exercice}


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%%%     Exercice 55
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{x+4}{9}-\frac{3x-1}{4}>\frac{x-2}{18}-\frac{1}{6}\]
\end{exercice}


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%%%     Exercice 56
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{2x-1}{2}-\frac{1}{3}\le 4\left(x+\frac{1}{2}\right)-(3x-1)\]
\end{exercice}


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%%%     Exercice 57
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre le système d'inéquation~:
\[\left\{
\begin{array}{ccc}
\frac{3x-5}{6}-\frac{1}{4}&\ge& \frac{2x+1}{3}-\frac{1}{12}\\
\frac{4x+3}{3}-\frac{1}{12}&<&\frac{x+2}{6}+\frac{1}{4}
\end{array}
\right.\]
\end{exercice}


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%%%     Exercice 58
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre~$m$~:
\[m(x-2)\ge 2x-1\]
\end{exercice}


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%%%     Exercice 59
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre~$m$~:
\[\frac{5m-3}{2}+mx<\frac{2}{3}+4m\]
\end{exercice}


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%%%     Exercice 60
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre~$m$~:
\[\frac{x}{m-2}>1+\frac{2x-1}{3}\]
\end{exercice}


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%%%     Exercice 61
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre~$m$~:
\[\left\{
\begin{array}{ccc}
3x-2&\ge& 3(x+2m)\\
5x-2m&\le& 4x-13+m
\end{array}
\right.\]
\end{exercice}


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%%%     Exercice 62
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre~$m$~:
\[\left\{
\begin{array}{ccc}
x+6m&\ge& 5(x-2)-3(m-5)\\
2m-2(x+3)&<& 3(m-4x)+11
\end{array}
\right.\]
\end{exercice}


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%%%     Exercice 85
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{4x+1}{3x-5}\ge 0\]
\end{exercice}


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%%%     Exercice 86
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[3x^2-x+8<0\]
\end{exercice}


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%%%     Exercice 84
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[(3x+1)(x+2)\le 2\]
\end{exercice}


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%%%     Exercice 87
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[(3x^2-2x-10)(x+1)<0\]
\end{exercice}


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%%%     Exercice 88
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[x-\frac{1}{x}>3\]
\end{exercice}


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%%%     Exercice 89
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{2x-3}{x^2-3x-10}\le 0\]
\end{exercice}


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%%%     Exercice 90
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{1}{x-1}-\frac{1}{2x-3}\ge \frac{6}{6x-7}\]
\end{exercice}


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%%%     Exercice 91
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{3x+2}{x^2-3x+2}<1\]
\end{exercice}


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%%%     Exercice 92
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{2x-7}{2(x-1)}-1\le \frac{1}{4-x}\]
\end{exercice}


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%%%     Exercice 93
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[\frac{x^3+7x-5}{(-x^2+x-3)(x+1)}\ge -1\]
\end{exercice}


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%%%     Exercice 94
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation~:
\[2<\frac{x-3}{x-5}\le 3\]
\end{exercice}


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%%%     Exercice 95
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre le système d'inéquations~:
\[
\left\{
\begin{array}{ccc}
x^2-2x-47 &>& 0\\
x^2-10x+16&\le& 0
\end{array}
\right.
\]
\end{exercice}


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%%%     Exercice 96
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre le système d'inéquations~:
\[
\left\{
\begin{array}{ccc}
(x-3)(-x^2+5x-4) &<& 0\\
x^2-3x-6&\ge& 0
\end{array}
\right.
\]
\end{exercice}


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%%%     Exercice 97
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation suivante en fonction du paramètre~$m$~:
\[x^2-(m+6)x-6m^2+13m+5>0\]
\end{exercice}


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%%%     Exercice 98
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation suivante en fonction du paramètre~$m$~:
\[mx^2-(m+2)x+m+17>0\]
\end{exercice}


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%%%     Exercice 98
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'inéquation suivante en fonction du paramètre~$m$~:
\[mx^2-(m+2)x+m+17>0\]
\end{exercice}


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%%%     Exercice 106
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[(-3x^2+x-7)(x^2-7)(4x^2+x+5)<0\]
\end{exercice}


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%%%     Exercice 107
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre le système~:
\[\left\{
\begin{array}{ccccc}
-2&<&\frac{15-x}{2x+3}&<&2\\
&\frac{x-1}{5x-9}&>&\frac{x+1}{x}&\\
&(x+2)^2&\le&25&
\end{array}
\right.\]
\end{exercice}


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%%%     Exercice 108
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Discuter suivant les valeurs de $m$ l'existence et le signe des racines de~:
\[(m-1)x^2+2m\sqrt 2 \, x -2m-3=0\]
\end{exercice}


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%%%     Exercice 109
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Discuter suivant les valeurs de $m$ l'existence et le signe des racines de~:
\[(m-5)x^2+(7m-1)x-4m+1=0\]
\end{exercice}


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%%%     Exercice 110
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Pour quelles valeurs de $m$ l'inéquation suivante admet-elle $\bf R$ pour ensemble de solutions~?
\[(m+3)x^2-2(m+1)x-(m+1)>0\]
\end{exercice}


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%%%     Exercice 111
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Pour quelles valeurs de $m$ l'équation suivante admet-elle deux racines distinctes et strictement positives~?
\[3x^2-5x+m+7=0\]
\end{exercice}


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%%%     Exercice 112
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Pour quelles valeurs de $m$ l'équation suivante admet-elle deux racines distinctes et strictement positives~?
\[(m-3)x^2+(1-2m)x+m+1=0\]
\end{exercice}

\label{fin}
\end{document}