INEQUATIONS
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Exercice 1
1) Demi-droite [AB) : \(x\geq -3\)
2) Demi-droite [BA) : \(x\leq 4\).
3) Segment [AB] : \(-3\leq x\leq 4\).
Exercice 2
\[
\begin{align*}
&x+7<4\\
&x<4-7\\
&x<-3
\end{align*}
\]
\[ \begin{align*} &x+1>-3\\ & x>-3-1 \\ & x>-4 \end{align*} \]
\[ \begin{align*} &x+1>-3\\ & x>-3-1 \\ & x>-4 \end{align*} \]
\[
\begin{align*}
&x-5\leq 7 \\
&x\leq 7+5 \\
&x\leq 12 \\
\end{align*}
\]
\[ \begin{align*} & -x+1\geq 5 \\ & -x\geq 5-1 \\ & -x\geq 4 \\ &\frac{-x}{-1} \color{red}\leq \frac{4}{-1}\\ & x\leq -4 \end{align*} \]
\[ \begin{align*} & -x+1\geq 5 \\ & -x\geq 5-1 \\ & -x\geq 4 \\ &\frac{-x}{-1} \color{red}\leq \frac{4}{-1}\\ & x\leq -4 \end{align*} \]
Exercice 3
\[
\begin{align*}
&3x+5<11\\
&3x<11-5 \\
&3x<6\\
&x<\frac{6}{3}\\
&x<2
\end{align*}
\]
\[ \begin{align*} & -2x+5>7 \\ & -2x>7-5 \\ & -2x>2 \\ & x \color{red} < \frac{2}{-2}\\ & x<-1 \end{align*} \]
\[ \begin{align*} & -2x+5>7 \\ & -2x>7-5 \\ & -2x>2 \\ & x \color{red} < \frac{2}{-2}\\ & x<-1 \end{align*} \]
\[
\begin{align*}
&4-5x\leq 10\\
&-5x\leq 10-4\\
&-5x\leq 6\\
&x \color{red} \geq \frac{6}{-5}\\
&x\geq -1.2
\end{align*}
\]
\[ \begin{align*} & 13-2x\geq 5\\ & -2x\geq 5-13 \\ & -2x\geq -8\\ & x \color{red}\leq \frac{-8}{-2}\\ \qquad & x\leq 4 \end{align*} \]
\[ \begin{align*} & 13-2x\geq 5\\ & -2x\geq 5-13 \\ & -2x\geq -8\\ & x \color{red}\leq \frac{-8}{-2}\\ \qquad & x\leq 4 \end{align*} \]
Exercice 4
\(1)\quad x<5\)
\(2)\quad x>-3\)
\(3)\quad x\leq-2\)
\(4)\quad x\geq 2\)
\(5)\quad 3\leq x\leq 5\)
\(6)\quad -4< x\leq 0\)
0 fait partie des solutions donc le crochet est tourné vers la zone verte.