SUP03-13

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a. \[\begin{aligned} 13 + \frac 32 x &= 1& \\ \iff \frac 32x &=1 - 13& \\ \iff \frac 32x &= -12& \\ \iff x &= -12\times\frac 23& \\ \iff x &=-8.& \end{aligned}\] Donc l'ensemble solution est $S = \{-8\}$.

b. \[\begin{aligned} 4x + \frac 13 &= \frac 12x + 2& \\ \iff 4x -\frac12x &= 2 - \frac 13& \\ \iff \frac72x &= \frac 53& \\ \iff x &= \frac 53 \times \frac 72& \\ \iff x &= \frac{35}6.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{\dfrac{35}6\right\}$.

c. \[\begin{aligned} \frac32x + \frac 14 &= \frac 74& \\ \iff \frac32x &= \frac74-\frac14& \\ \iff \frac32x &= \frac64& \\ \iff \frac 32x &= \frac32& \\ \iff x &= \frac32\times \frac 23& \\ \iff x&=1.& \end{aligned}\] Donc l'ensemble solution est $S = \{1\}$.

d. \[\begin{aligned} \frac{x-3}5 &= \frac38& \\ \iff x-3 &= \frac 38 \times 5& \\ \iff x-3 &=\frac{15}8& \\ \iff x &= \frac{15}8+3& \\ \iff x&=\frac{39}8.& \end{aligned}\] Donc l'ensemble solution est $S = \left\{\dfrac{39}8\right\}$.

e. \[\begin{aligned} \frac{2x-3}7 &= \frac{x-1}3& \\ \iff 3(2x-3) &= 7(x - 1)& \\ \iff 6x - 9 &= 7x - 7& \\ \iff 6x - 7x &= -7 + 9& \\ \iff -x &= 2& \\ \iff x &= -2.& \end{aligned}\] Donc l'ensemble solution est $S = \{-2\}$.

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code : 190