Explications étape par étape:
• 2(x-4) < 3(2x-1) <=> 2x-8 < 6x-3 <=> -4x < 5
<=> x > -5/4
donc S= ]-5/4 ; +infini[
• 3x+1 >= 0 <=> x >= 1/3
donc S= [1/3 ; +infini[
• (x+3)/4 - (1+x)/2 > 0 <=> (x+3)/4 > (1+x)/2
<=> x+3 > (1+x)/2 *4/1 (4=4/1)
<=> x+3 > (4x+4)/2
<=> x+3 > 2x+2
<=> 1 > x
donc S= ]-infini ; 1[
• (x+2)/3 =< (1/2)*x <=> x+2 =< (3/2)*x
<=> 2 =< (3/2)x - 1x (1x=(2/2)*x)
<=> 2 =< (1/2)*x
<=> 4 =< x
donc S= [4 ; +infini[
