Réponse :
résoudre les équations
a) 5 x + 2 = 9 x + 7 ⇔ - 5 = 4 x ⇔ x = - 5/4 ⇔ S = {- 5/4}
b) 2(x - 1) - 3(x + 1) = 4(x - 2)
2 x - 2 - 3 x - 3 = 4 x - 8
- x - 5 = 4 x - 8 ⇔ - 5 + 8 = 4 x + x ⇔ 3 = 5 x ⇔ x = 3/5 ⇔ S = {3/5}
c) (x + 2)(x + 1) = (x + 4)(x - 5)
x² + 3 x + 2 = x² - x - 20
3 x + 2 = - x - 20
4 x = - 22 ⇔ x = - 22/4 = - 11/2 ⇔ S = {- 11/2}
d) - 1/2) x + 3 = x - 7
10 = x + 1/2) x
10 = 3/2) x ⇔ x = 20/3 ⇔ S = {20/3}
e) 7 x - 1/4 = 5/11
7 x = 5/11 + 1/4
7 x = 20/44 + 11/44
7 x = 31/44 ⇔ x = 31/308 ⇔ S = {31/308}
f) (2 x + 3)/6 - (x - 1)/6 = (x + 2)/3 + 2
(2 x + 3)/6 - (x - 1)/6 = 2(x + 2)/6 + 12/6
(2 x + 3) - (x - 1) = 2(x + 2) + 12
2 x + 3 - x + 1 = 2 x + 4 + 12
x + 4 = 2 x + 16
4 - 16 = x ⇔ x = - 12 ⇔ S = {- 12}
g) (2 x + 3)/2 = (7 x - 2)/3
3(2 x + 3)/6 = 2(7 x - 2)/6
3(2 x + 3) = 2(7 x - 2)
6 x + 9 = 14 x - 4
9 +4 = 14 x - 6 x
13 = 8 x ⇔ x = 13/8 ⇔ S = {13/8}
Explications étape par étape :
