Linearne nejednacine autor Marko Mikovi Resi nejednacine a

Linearne nejednacine autor Marko Mišković

Resi nejednacine: a) 15 x+6<51 b) -8(x-3)+15(x-2) ≥ 15 a) 15 x+6<51 15 x<51 -6 15 x<45 x<3 b) -8(x-3)+15(x-2) ≥ 15 -8 x+24+15 x-30≥ 15 -8 x+15 x≥ 15+30 -24 7 x≥ 21 x≥ 3 3 3

Reši nejednačine a) 14+(35+x) ≥ 12 b) 33 -(x-120) ≤ 23 a) 14+(35+x) ≥ 12 14+35+x ≥ 12 -14 -35 x ≥-2 -35 x ≥-37 b) 33 -(x-120) ≤ 23 33 -x+120 ≤ 23 -x ≤ 23 -33 -120 -x ≤-10 -120 -x ≤-130/ ·(-1) x ≥ 130 -37 130

Reši nejednačine: a) 3(x+2)-2(1 -x)>4 x+5 b) 5(2 x-1)-3(4 x+5)<-3 x+11 a) 3(x+2)-2(1 -x)>4 x+5 3 x+6 -2+2 x>4 x+5 3 x+2 x-4 x>5 -6+2 5 x-4 x>-1+2 x>1 b) 5(2 x-1)-3(4 x-5)<-3 x+11 10 x-5 -12 x+15<-3 x+11 10 x-12 x+3 x<11+5 -15 -2 x+3 x<16 -15 x<1

Za koje vrednosti promenljive x važi da je A≤B, ako je: A= 3 x-1 -[2 x-4 -(x+1)] B=x+6 3 x-1 - [2 x-4 -(x+1)] ≤x+6 3 x-1 - [2 x-4 -x-1] ≤x+6 3 x-1 -2 x+4+x+1 ≤x+6 3 x-2 x ≤ 6 -1+1 -4 x ≤ 5 -3 x ≤ 2

Reši nejednačine: a) |5 -2 x|<1 b) 2|x+1|>x+4 a) |5 -2 x|<1 |5 -2 x| 5 -2 x≥ 0, -2 x≥-5 /(-1), x≤ 5/2 -(5 -2 x) 5 -2 x<0, -2 x<-5 /(-1), x>5/2 -(5 -2 x) 5/2

x ≤ 5/2 -(5 -2 x)<1 -5+2 x<1+5 2 x<6 x<3 x∈ (2, 3) x>5/2 (5 -2 x)<1 5 -2 x<1 -5 -2 x<-4/(-1) x>2

b) 2|x+1|>x+4 |x+1| x+1 ≥ 0, x ≥-1 -(x+1) x+1<0, x<-1 -(x+1) -1

2(-(x+1))>x+4 2(-x-1)>x+4 -2 x-2>x+4 -2 x-x>4+2 -3 x>6/(-1) 3 x<-6 x<-2 2(x+1)>x+4 2 x+2>x+4 2 x-x>4 -2 x>2 x∈ (-∞, 2) ∪ x∈(2, ∞)

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