Exercice 7 :

a.

[tex]\frac{-x+5}{2} =\frac{7x+5}{4} \\\frac{-2x+10}{4} =\frac{7x+5}{4} \\\\-2x+10= 7x +5\\-2x-7x = 5-10\\ -9x = -5\\x = \frac{5}{9}[/tex]

[tex]\frac{5}{9}[/tex]   est la solution de l'équation.

b.

[tex]\frac{x+7}{4}= 2x-1\\ x+7 = 4(2x-1)\\x+7 = 8x -4\\x-8x = -4-7\\-7x = -11\\x = \frac{11}{7}[/tex]

[tex]\frac{11}{7}[/tex]  est la solution de l'équation.

c.

[tex]2+7x= \frac{4-3x}{5}\\5(2+7x)= 4-3x\\10 +35x= 4-3x\\35x+3x= 4-10\\38x = -6\\x = \frac{-6}{38} \\x = \frac{-3}{19}[/tex]

[tex]\frac{-3}{19}[/tex]  est la solution de l'équation.

Explications étape par étape:

a) (-x +5) x4 = (7x+5) ×2

-4x +20 = 14x + 10

20 -10 = 14x + 4x

10 = 18x. x= 10/18 = 5/9

b) 5x + 7 = (2x-1) × 4

5x +7 = 8x - 4

7 + 4 = 8x - 5x

11 = 3x. x = 11/3

c) (2+7x) × 5 = 4 -3x

10 + 35x = 4 - 3x

35x + 3x = 4 -10

38x = -6. x = -6/38 = -3/19