Réponse :

résoudre

a) 5(3 - (2/3) x) = 2(x - 6) + 11/3  ⇔ 15 - (10/3) x = 2 x - 12 + 11/3

⇔ 2 x + (10/3) x = 15 + 12 - 11/3 ⇔ 6/3) x + (10/3) x = 81/3 - (11/3)

⇔ 16/3) x = 70/3 ⇔ x = 70/16 = 35/8  ⇔ S = {35/8}

b) (2 - 4 x)/5 - (3 x + 2)/4 = (1 - 9 x)/3

⇔ 12(2 - 4 x)/60 - 15(3 x + 2)/60 = 20(1 - 9 x)/60

⇔ (24 - 48 x - 45 x - 30)/60 = (20 - 180 x)/60

⇔ - 93 x - 6 = 20 - 180 x  ⇔ 87 x = 26 ⇔ x = 26/87 ⇔ S = {26/87}

c) 5/4) x + 3 ≤ 3/7) x - 2 ⇔ 5/4) x - (3/7) x ≤ - 5

⇔ 35/28) x - (12/38) x ≤ - 5 ⇔ 23/28) x ≤ - 5 ⇔ x ≤ - 140/23

⇔ S = ]-∞ ; - 140/23]

d) 1/4(x + 7) > x/3) + 1 ⇔ 1/4) x + (7/4) > x/3 + 1 ⇔  7/4  - 1 > x/3 - (1/4) x

⇔ 3/4 > x/12 ⇔ x/12 < 3/4 ⇔ x < 9 ⇔ S = ]- ∞ ; 9[

e) (- 3 x + 7) - (6 x + 2) ≥ 0 ⇔ - 3 x + 7 - 6 x - 2 ≥ 0 ⇔ - 9 x + 5 ≥ 0

⇔ 9 x ≤ 5 ⇔ x ≤ 5/9 ⇔ S = ]- ∞ ; 5/9]  

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