103 lines
4.0 KiB
TeX
103 lines
4.0 KiB
TeX
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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
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%\usepackage{multicol}
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\usepackage{tikz}
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\usepackage{fancybox}
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% Title Page
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\title{Inéquations 3 - Exercices}
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\author{}
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\date{}
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\fancyhead[L]{Troisième}
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\fancyhead[C]{\Thetitle}
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\fancyhead[R]{\thepage}
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\begin{document}
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\thispagestyle{fancy}
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\begin{Exo}
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\begin{center}
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\framebox{\parbox{0.45\textwidth}{
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Résoudre l'inéquation $3x + 5 > 0$ et représenter graphiquement les solutions.
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\begin{eqnarray*}
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3x + 5 > 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 5} \\
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3x + 5 \mathbf{+ (-5)} > \mathbf{-5} && \\
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3x > -5 & \hspace{1cm} & \mbox{On multiplie par l'inverse de 3 \colorbox{lightgray}{positif}} \\
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\mathbf{\frac{1}{3} \times }3x > \mathbf{ \frac{1}{3} \times }(-5) && \mbox{On ne change pas le sens de l'inégalité}\\
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x > \frac{-5}{3}
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\end{eqnarray*}
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La solution est $x > \frac{-5}{3}$.
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\begin{tikzpicture}
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\draw[->, very thick] (-5,0) -- (6,0);
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\foreach \x in {-5,-4,...,5} {
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\draw(\x,0) node[below] {\x} node {|};
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}
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\draw[color=red, line width = 5pt] ({-5/3}, 0) node[scale=2.5]{]} node[above left, scale = 1.3] {$\frac{-5}{3}$} -- (6,0);
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\end{tikzpicture}
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}}
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\end{center}
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\begin{center}
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\framebox{\parbox{0.45\textwidth}{
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Résoudre l'inéquation $-5x + 4 > 0$ et représenter graphiquement les solutions.
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\begin{eqnarray*}
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-5x + 4 > 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 4} \\
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-5x + 4 \mathbf{+ (-4)} > \mathbf{-4} && \\
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-5x > -4 & \hspace{1cm} & \mbox{On multiplie par l'inverse de -5 \colorbox{lightgray}{négatif}} \\
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\mathbf{\frac{1}{-5} \times }-5x \colorbox{lightgray}{<} \mathbf{ \frac{1}{-5} \times }(-4) && \mbox{On a changé le sens de l'inégalité}\\
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x < \frac{-4}{-5} = \frac{4}{5}
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\end{eqnarray*}
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La solution est $x < \frac{4}{5}$.
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\begin{tikzpicture}
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\draw[->, very thick] (-2,0) -- (6,0);
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\foreach \x in {-2,-1,...,5} {
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\draw(\x,0) node[below] {\x} node {|};
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}
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\draw[color=red, line width = 5pt] (-2,0) --({4/5}, 0)node[scale=2.5]{[} node[above right, scale = 1.3] {$\frac{4}{5}$} ;
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\end{tikzpicture}
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}}
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\end{center}
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\begin{enumerate}
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\item Résoudre puis représenter les solutions de l'inéquation $4x + 7 > 0$.
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\begin{eqnarray*}
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4x + 7 > 0 & \hspace{0.5cm} & \mbox{On ajoute l'opposé de \parbox{1cm}{\dotfill}} \\[0.5cm]
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4x + 7 + \parbox{1.5cm}{\dotfill}> \parbox{1.5cm}{\dotfill}&& \\[0.5cm]
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4x > \parbox{1cm}{\dotfill}& \hspace{0.5cm} & \mbox{On multiplie par l'inverse de \parbox{1cm}{\dotfill}} \\[0.5cm]
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\parbox{1.5cm}{\dotfill} \times 4x \ovalbox{\begin{minipage}{0.3cm}\hfill\vspace{0.5cm}\end{minipage}} \parbox{1.5cm}{\dotfill} \times \parbox{1cm}{\dotfill} && \mbox{On \parbox{2cm}{\dotfill} le sens de l'inégalité} \\[0.5cm]
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x \ovalbox{\begin{minipage}{0.3cm}\hfill\vspace{0.5cm}\end{minipage}} \frac{\parbox{1cm}{\dotfill}}{\parbox{1cm}{\dotfill}}
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\end{eqnarray*}
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La solution est \parbox{2cm}{\dotfill}.
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\\[0.5cm]
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\begin{tikzpicture}
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\draw[->, very thick] (-4,0) -- (6,0);
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\foreach \x in {-4,-3,...,5} {
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\draw(\x,0) node[below] {\x} node {|};
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}
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\end{tikzpicture}
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\item Résoudre puis représenter les solutions des inéquations suivantes
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\begin{enumerate}
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\item $3x + 2 \geq 0$
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\item $5x - 10 \leq 0$
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\item $-3x + 9 > 0$
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\item $-2 x - 6 < 0$
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\item $3x + 4 > 7 $
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\item $-5x - 8 \geq 2$
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\end{enumerate}
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\end{enumerate}
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\end{Exo}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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