Exercice 5 "Équation de la forme ax+b = cx+d Résoudre dans QQ chacune des équations suivantes. a) 2x+3 = 4x+5 b) 2x-3 =-4x+52 c) -2x+3,5 = 4x-5 d) -2x-3 =-4x+5 e) -4x+3 = 5-6x f) -3-4x = -1 + 6x g) 3x-4 = 8x -3 h) -5x+7 = 6-5x i) 2x-2 = -10 + 2x​

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Explications étape par étape:

[tex]a. \: 2x + 3 = 4x + 5 \\ 2x - 4x = 5 - 3 \\ - 2x = 2 \\ x = \frac{2}{ - 2} \\ x = - 1 \\ b \: .\: 2x - 3 = - 4x + 52 \\ 2x + 4x = 52 + 3 \\ 6x = 55 \\ x = \frac{55}{6} \\ c. - 2x + 3.5 = 4x - 5 \\ - 2x - 4x = - 5 - 3.5 \\ - 6x = - 8 \\ x = \frac{8}{6} \\ x = \frac{4}{3} \\ d. \: - 2x - 3 = - 4x + 5 \\ - 2x + 4x = 5 + 3 \\ 2x = 8 \\ x = \frac{8}{2} \\ x = 4 \\ e. \: \: - 4x + 3 = 5 - 6x \\ - 4x + 6x = 5 - 3 \\ 2x = 2 \\ x = \frac{2}{2} \\ x = 1 \\ f. \: - 3 - 4x = - 1 + 6x \\ - 4x - 6x = - 1 + 3 \\ - 10x = 2 \\ x = \frac{ - 2}{10} \\ x = \frac{ - 1}{5} \\ g. \: 3x - 4 = 8x - 3 \\ 3x - 8x = - 3 + 4 \\ - 5x = 1 \\ x = \frac{ - 1}{5} \\ h. \: - 5x + 7 = 6 - 5x \\ - 5x + 5x = 6 - 7 \\ 0 = - 1 \: impossible \: donc \: pas \: de \: solution.[/tex]

2x-2=-10+2x

2x-2x=-10+2

0=-8 impossible donc pas de solutions