SUP03-12

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a. \[\begin{aligned} 2x - 3 &= 5& \\ \iff 2x &= 5 + 3& \\ \iff 2x &= 8& \\ \iff x &= \frac 82& \\ \iff x &=4.& \end{aligned}\] Donc l'ensemble solution est $S=\{4\}$.

b. \[\begin{aligned} x + 4 &= 5x - 2& \\ \iff x - 5x &= -4 - 2& \\ \iff -4x &= -6& \\ \iff x &= \frac{-6}{-4}& \\ \iff x &= \frac 3 2.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{\dfrac 32 \right\}$.

c. \[\begin{aligned} 3(x+1) &= 5x - 1& \\ \iff 3x + 3 &= 5x - 1& \\ \iff 3x - 5x &= -1 - 3& \\ \iff -2x &= -4& \\ \iff x &= \frac{-4}{-2}& \\ \iff x &= 2.& \end{aligned}\] Donc l'ensemble solution est $S = \{2\}$.

d. \[\begin{aligned} -2(4 - x) + 1 &= 2& \\ \iff -8 + 2x + 1&= 2& \\ \iff 2x &= 2 -1 + 8& \\ \iff 2x &= 9& \\ \iff x &= \frac 92.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{\dfrac92\right\}$.

e. \[\begin{aligned} \frac 23x &= 4& \\ \iff x&= 4\times \frac 3 2& \\ \iff x &= 6.& \end{aligned}\] Donc l'ensemble solution est $S = \{6\}$.

f. \[\begin{aligned} -3x &= 4& \\ \iff x &= \frac{4}{-3}& \\ \iff x &= -\frac 4 3.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{-\dfrac 43\right\}$.

g. \[\begin{aligned} 2(3x - 1) - 5 &= x + 1& \\ \iff 6x -2 - 5 &= x + 1& \\ \iff 6x - x &= 1 +2 + 5& \\ \iff 5x &= 8& \\ \iff x &= \frac 85.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{\dfrac85\right\}$.

h. \[\begin{aligned} -3x + 4 &= 2\left(x + \frac 2 5\right)& \\ \iff -3x + 4 = 2x + \frac 45& \\ \iff -3x -2x &= -4 +\frac 45& \\ \iff -5x &= -\frac{16}{5}& \\ \iff x &= -\frac{16}{5}\times \left(-\frac 1 5\right)& \\ \iff x &= \frac{16}{25}.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{\dfrac{16}{25}\right\}$.

i. \[\begin{aligned} 3(x-2) &= -2(x + 4)& \\ \iff 3x - 6 &= -2x - 8& \\ \iff 3x + 2x &= -8 + 6& \\ \iff 5x &= -2& \\ \iff x &= -\frac 2 5.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{-\dfrac 25\right\}$.

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code : 189