Réponse :

Explications étape par étape :

Exercice 2)

-11 < -7 → 2x -11 < 2x - 7

ou 2x - 11 - (2x - 7) = 2x - 11 - 2x + 7 = -4 < 0

→ 2x -11 - (2x - 7) < 0 → 2x - 11 < 2x - 7

3/2 > 7/6 → 3x + 3/2 > 3x + 7/6 ou

(3/5)x + 3/2 - ((3/5)x + 7/6) = (3/5)x + 3/2  - (3/5)x - 7/6 = 1/3 > 0

(3/5)x + 3/2 - ((3/5)x + 7/6) > 0 → 3x + 3/2 > 3x + 7/6

x² - 4(x-1) = x² - 4x + 4 = (x - 2)² ≥ 0 → x² - 4(x-1) ≥ 0 → x² ≥ 4(x-1)

Exercice 6)

-4x +7 < 13 → -4x < 13-7 → -4x < 6 → x > 3/2 → S = ]3/2 ; +∞[

6x + 8 ≥ 9 - (x -14) → 6x + 8 ≥ 9 - x + 14 → 6x + x ≥ 9 + 14 - 8

→7x ≥ 15 → x ≥ 15/7  → S = [15/7 ; +∞[

9(x-3) - 2x > 7(x + 1) → 9x - 27 - 2x > 7x  + 7 → 7x - 7x > 7 + 27

→ 0 > 34 impossible  S = ∅

3x - 5(2x + 4) < -5(x - 1) - 11 → 3x - 10x - 20 < -5x + 5 - 11

→ 3x - 10x + 5x < 5 - 11 + 20 → -2x < 14 → x > 14/(-2) → x > -7

S = -7 ; +∞[

1 - (x-3)/5 > x + (5 - 2x)/2 → (10 - 2(x - 3))/10 > (10x+ 5(5 - 2x))/10

→10 - 2x + 6 > 10x + 25 -10x → -2x -10x + 10x > 25 -10 - 6

→ -2x > 9 → x < 9/(-2) → x < -9/2 → S = ]-∞ ; -9/2[

(3(5x + 1)) /12 - 12x/12 ≤ (-6(x + 4))/12

→ (15x + 3)/12 - 12x/12 ≤ (-6x - 24)/12→15x + 3 - 12x ≤ -6x - 24

→15x - 12x + 6x ≤ -24 - 3→ 9x < -27 → x < -27/9  → x < -3

S = ]-∞ ; -3[