Bonjour,
Résoudre les inéquations:
(4x-1)/(2x+3) ≥ 3
2x+3 ≠ 0 ; x≠ -3/2
(4x-1)/(2x+3) - 3 ≥ 0
[ 4x-1-3(2x+3) ] / (2x+3) ≥ 0
(4x-1-6x-9)/(2x+3) ≥ 0
(-2x-10) / (2x+3) ≥ 0
-2x-10= 0; x= -10/2= -5
Tableau de signes:
x -5 -3/2
-2x-10 + 0 - II -
2X+3 - I - II +
Q - 0 + II -
S= [ -5 ; -3/2 [
2x/(6x+1) < 2
2x/(6x+1) - 2 < 0
[2x- 2(6x+1) ] / (6x+1) < 0
(2x-12x-2) / (6x+1) < 0
(-10x -2 ) / (6x+1) < 0
6x+1 ≠ 0 ; x ≠ -1/6 ***-1/6= -0.167 et -1/5= -0.2
-10x-2= 0; x= -2/10= -1/5
x -1/5 -1/6
-10x-2 + 0 - II -
6x+1 - I - II +
Q - 0 + II -
S= ] - ∞; -1/5 [ U ] -1/6; +∞ [
