Réponse :
Explications étape par étape
| x | > a
x < -a ∪ x > a
ex 1: | x + 5 | > 3
x + 5 < -3 ∪ x + 5 > 3
x < -8 ∪ x > - 2
S = ] - ∞ , -8 [ ∪ ] -2 , +∞ [
ex 2: | 3x - 2 | ≥ 4
3x - 2 ≤ -4 ∪ 3x - 2 ≥ 4
3x ≤ -2 ∪ 3x ≥ 6
x ≤ -2/3 ∪ x ≥ 2
S = ] -∞ , -2/3 ] ∪ [ 2, +∞ [
| x | < a
-a < x < a
ex 1: | x - 3 | ≤ 12
-12 ≤ x - 3 ≤ 12
-12 + 3 ≤ x ≤ 12 + 3
-9 ≤ x ≤ 15
S = [ -9 , 15 ]
Ex 2: | 4x - 2 | < 8
- 8 < 4x - 2 < 8
- 8 + 2 < 4x < 8 + 2
-6 < 4x < 10
-6/4 < x < 10/4
-3/2 < x < 5/2
S = ] -3/2 , 5/2 [