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Résoudre dans ℝ les équations suivantes :
-
$3 - (5x +1) = 8x + (4-2x)$;
Corrigé
\[\begin{aligned}
&3 - (5x +1) = 8x + (4-2x)&
\\ \iff
&3 -5x - 1 = 8x + 4 - 2x&
\\ \iff
&-5x - 8x + 2x = 4 - 3&
\\ \iff
&-11x = 1&
\\ \iff
&x = -\frac 1 {11}.&
\end{aligned}\]
Donc $S = \left\{-\dfrac 1 {11}\right\}$.
-
$8 - 3(2x - 4) = 5x - (x+1)$;
Corrigé
\[\begin{aligned}
&8 - 3(2x - 4) = 5x - (x+1)&
\\ \iff
&8 - 6x + 12 = 5x -x - 1&
\\ \iff
&-6x-5x+x = -8 -12 - 1&
\\ \iff
&-10x = -21&
\\ \iff
&x = \dfrac{-21}{-10}&
\\ \iff
&x =\frac{21}{10}.&
\end{aligned}\]
Donc $S = \left\{\dfrac{21}{10}\right\}$.
-
$8 + (3x - 2) = 5x - (3x - 5)$;
Corrigé
\[\begin{aligned}
&8 + (3x - 2) = 5x - (3x - 5)&
\\ \iff
&8 + 3x - 2 = 5x - 3x + 5&
\\ \iff
&3x -5x + 3x = -8 +2 + 5&
\\ \iff
&x = -1&
\end{aligned}\]
Donc $S = \big\{-1\big\}$.
-
$4(2x-6) - 8 = 5 - (x - 7)$.
Corrigé
\[\begin{aligned}
&4(2x-6) - 8 = 5 - (x - 7)&
\\ \iff
&8x - 24 - 8 = 5 - x + 7&
\\ \iff
&8x+x = 24 + 8 +5 + 7&
\\ \iff
&9x = 30&
\\ \iff
&x = \frac{30}{9}&
\\ \iff
&x = \frac {10} 3.&
\end{aligned}\]
Donc $S = \left\{\dfrac{10} 3\right\}$.
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