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Résoudre dans ℝ les équations suivantes :
\[3x + 2 =0\;;\]
Corrigé
\[\begin{aligned}
&3x + 2 = 0&
\\
\iff &3x = -2&
\\
\iff &x = -\dfrac 2 3.&
\end{aligned}\]
Donc $S = \left\{-\dfrac 2 3\right\}$.
\[4 - 5x = 0\;;\]
Corrigé
\[\begin{aligned}
&4 - 5x = 0&
\\
\iff &-5x = -4&
\\
\iff &x = \dfrac{-4}{-5}&
\\
\iff &x = \dfrac 4 5.&
\end{aligned}\]
Donc $S = \left\{\dfrac 4 5\right\}$.
\[7x + 8 = 0\;;\]
Corrigé
\[\begin{aligned}
&7x + 8 = 0&
\\
\iff &7x = -8&
\\
\iff &x = -\dfrac 8 7.&
\end{aligned}\]
Donc $S = \left\{-\dfrac 8 7\right\}$.
\[9x - 4 = 0\;;\]
Corrigé
\[\begin{aligned}
&9x - 4 = 0&
\\
\iff &9x = 4&
\\
\iff &x = \dfrac 4 9.&
\end{aligned}\]
Donc $S = \left\{\dfrac 4 9\right\}$.
\[5x + 4 = 4\;;\]
Corrigé
\[\begin{aligned}
&5x + 4 = 4&
\\ \iff
&5x = 4 - 4&
\\ \iff
&5x = 0&
\\ \iff
&x = \dfrac 0 5 = 0.&
\end{aligned}\]
Donc $S = \{0\}$.
\[3x - 2 = 11.\]
Corrigé
\[\begin{aligned}
&3x - 2 = 11&
\\ \iff
&3x = 11 + 2&
\\ \iff
&3x = 13&
\\ \iff
&x = \dfrac{13} 3.&
\end{aligned}\]
Donc $S = \left\{\dfrac{13} 3\right\}$.
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