Exercice 6 Résoudre les équations suivantes: 1. 4x - 2 = 5x - 3 2. 6 + 8x = 4x - 1 3. 6x-7 = 9 + 14x 4. 3x +2 = 5 - 7x 5. 2(8x-3) =3(5x +8 ) 6. 4(x-3)+ (6x -9)

Réponse :

1) 4x - 2 = 5x - 3

4x - 2 + 3 = 5x - 3 + 3

4x + 1 = 5x

4x - 4x + 1 = 5x - 4x

1 = x

2) 6 + 8x = 4x - 1

6 + 8x - 6 = 4x - 1 - 6

8x = 4x - 7

8x - 4x = 4x - 7 - 4x

4x = -7

4x/4 = -7/4

x = -7/4

3) 6x - 7 = 9 + 14x

6x - 7 + 7 = 9 + 14x + 7

6x = 16 + 14x

6x - 14x = 16 + 14x - 14x

-8x = 16

-8x / -8 = 16 / -8

x = -2

4) 3x + 2 = 5 - 7x

3x + 2 - 2 = 5 - 7x - 2

3x = 3 - 7x

3x + 7x = 3 - 7x + 7x

10x = 3

10x / 10 = 3 / 10

x = 3/10

5) 2(8x-3) =3(5x +8)

2 x 8x - 2 x 3 = 3 x 5x + 3 x 8

16x - 6 = 15x + 24

16x - 6 + 6 = 15x + 24 + 6

16x = 15x + 30

16x - 15x = 15x + 30 - 15x

x = 30

6) 4(x-3)+ (6x -9) = 2(8x -4) - (6x -3)​

4x - 4 x 3 + (6x -9) = 2 x 8x - 2 x 4 - (6x -3)​

4x - 12 + 6x - 9 = 16x - 8 + 6x + 3

4x + 6x - 12 - 9 = 16x + 6x - 8 + 3

10x - 21 = 22x - 5

10x - 21 + 21 = 22x - 5 + 21

10x = 22x + 16

10x - 22x = 22x + 16 - 22

-12x = 16

-12x / -12 = 16 / -12

x = -16/12