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1. Sa se rezolve inecuatiile:
a) 4x-5/x+3 ≤ 1
b) 2-3x/x-1 ≥ -2
c) 2/x-1 + 5x-3/x-1 ≥ 1
d) 1/2(x+2) - 2x+1/x+2 < 1/2
e) (x+4)(x+1)/2x+3> 0
f) (-x-3)(x+5)/x-2< 0


Răspuns :

a)4x-5/x+3≤1⇒4x-5≤x+3⇒4x-x≤5+3⇒3x≤8⇒x≤8/3
b)2-3x/x-1≥-2⇒2-3x≥-2(x-1)⇒2-3x≥-2x+2⇒2x-3x≥0⇒-x⇒0/-1⇒x=0
c)2/x-1+5x-3/x-1≥1⇒
2+5x-3/x-1≥1⇒
5x-1/x-1≥1⇒5x-1≥x-1⇒5x-x≥0⇒4x≥0⇒x≥0
d)1/2(x-2)-2x+1/x+2>1/2
1/2x+4-2x+1/x+2<1/2⇒1-4x+2/2x+4<1/2⇒3-4x/2x+4<1/2⇒2(3-4x)<2x-4⇒
6-8x<2x-4⇒-8x-2x<-6-4⇒-10x<-10⇒x<-10/-10⇒x<1
sucees