Réponse :
Bonjour,
Exercice 1
[tex]A = -2 \times 3^2 - (4 - 7 \times 3)\\\\= -2 \times 9 - (4 - 21)\\\\= -18 - (-17)\\\\= -18 + 17\\\\= -1[/tex]
[tex]B = \dfrac{3}{5} - \dfrac{2}{3} + \dfrac{1}{2}\\\\= \dfrac{3 \times 6}{5 \times 6} - \dfrac{2 \times 10}{3 \times 10} + \dfrac{1 \times 15}{2 \times 15}\\\\= \dfrac{18}{30} - \dfrac{20}{30} + \dfrac{15}{30}\\\\= -\dfrac{2}{30} + \dfrac{15}{30}\\\\= \dfrac{13}{30}[/tex]
[tex]C = \dfrac{-3}{5} \times \left(\dfrac{2}{3} - 1 \right)\\\\= -\dfrac{3}{5} \times \left(\dfrac{2}{3} - \dfrac{3}{3} \right)\\\\= -\dfrac{3}{5} \times \left (-\dfrac{1}{3} \right)\\\\= \dfrac{1}{5}[/tex]
[tex]D = \dfrac{\dfrac{5}{4}}{1 + \dfrac{2}{3}}= \dfrac{\dfrac{5}{4}}{\dfrac{3}{3} + \dfrac{2}{3}}\\\\\\= \dfrac{\dfrac{5}{4}}{\dfrac{5}{3}} = \dfrac{5}{4} \times \dfrac{3}{5}\\\\\\= \dfrac{3}{4}[/tex]
Exercice 2
[tex]I = (x - 3) - (4 - 2x)\\\\= x - 3 - 4 + 2x\\\\= x + 2x - 3 - 4\\\\= 3x - 7[/tex]
[tex]J = 3x \times (2x - 5)\\\\= 3x \times 2x - 3x \times 5\\\\= 6x^2 - 15x[/tex]
[tex]K = (x + 3) \times (1 - x)\\\\= x \times 1 - x \times x + 3 \times 1 - 3 \times x\\\\= x - x^2 + 3 - 3x\\\\= -x^2 + x - 3x + 3\\\\= -x^2 - 2x + 3[/tex]
[tex]L = (2x + 3) \times (5x + 1)\\\\= 2x \times 5x + 2x \times 1 + 3 \times 5x + 3 \times 1\\\\= 10x^2 + 2x + 15x + 3\\\\= 10x^2 + 17x + 3[/tex]
Exercice 3
[tex]2x + 2 = 0\\\\2x = -2\\\\x = -\dfrac{2}{2}\\\\x = -1[/tex]
[tex]-3x + 4 = 1\\\\-3x = 1 - 4\\\\-3x = -3\\\\x = \dfrac{-3}{-3}\\\\x = 1[/tex]
[tex]-2x + 1 = 3x + 2\\\\-2x - 3x = 2 - 1\\\\-5x = 1\\\\x = -\dfrac{1}{5}[/tex]
