Réponse :
Explications étape par étape
a.
(5/2)x + 4 > x +6 <=> 5/2 x - x > 6 -4
<=> ((5/2)-1)x > 2
<=> ((5-2*1)/2)x > 2
<=> 3x > 2*2
<=> x > 4/3 alors x ∈ ]4/3; +∞[
b.
(14/3)x ≤ 2x -1/3 <=> ((14/3) -2)x ≤ -1/3
<=> ( (14 -2*3)/3)x ≤ -1/3
<=> 8x ≤ -(3*1) / 3 or -(3*1) / 3= -1
<=> x ≤ -8 alors x ∈ ]-∞;-8]
c. (7/9)x +4 ≥ (1/3)x - 3 <=> (7/9)x - (1/3)x ≥ - 3 -4
<=> ((7 - 3*3)/9)x ≥ -7
<=> ( 1 )x ≥ -7 * 9
<=> x ≥ - 63 alors x ∈ [-63; +∞[
d. (-1/2)x - 1 < (1/5)x + (1/4) <=> (-1/2)x - (1/5)x < (1/4) +1
<=> ((-1*5) - 1*2)/ 10)x < (1+4)/4
<=> -7x < 10* (5/4)
<=> x < (25/2) /7
<=> x < 25/14 alors x ∈ ]-∞; 25/14 [
j'espère avoir aidé.
