Question

rezolvati in R inecuatiile :
a) 3(x-1)<5(x+3)
b) 4(2x+1)-2(3x+2) < 0
c) 2x-3(2-2x)>2
d) 8x-5(2x-4)<10
e) 9x+4-5(2x+1)<3
f) 2x-3(x+1)>x+5
g) 7x-4(3+2x) >x
h) 2x+3-3(x+1)<1-x

Answer 1

a) 3(x-1)<5(x+3)
3x-3<5x+15
3x-5x<15+3
2x<18
x<18/2
x<9

b) 4(2x+1)-2(3x+2) < 0
8x+4-6x-4<0
2x<0
x<0

c) 2x-3(2-2x)>2
2x-6+6x>2
4x>2+6
x>8/4
x>2

d) 8x-5(2x-4)<10
8x-10x+20<10
-2x<-20+10
-x<-10/2
-x<-5    inmultim -1
x>5

e) 9x+4-5(2x+1)<3
9x+4-10x-5<3
-x-1<3
-x<3-1
-x<2    inmultim -1
x>-2

f) 2x-3(x+1)>x+5
2x-3x-3>x+5
-x-x>5+3
-2x>8
-x>8/2     inmultim -1
x<-4

g) 7x-4(3+2x) >x
7x-12-8x>x
-x-x>12
-2x>12
-x<12/2
-x>6    inmultim -1
x<-6

h) 2x+3-3(x+1)<1-x
2x+3-3x-3<1-x
-x+x<1
0<1 nu are solutii

Answer 2

pff cat ai de scris.....
a)3x-3<5x+15 =>> 3x-5x<3+15 =>> -2x < 18 =>> x<-9 =>> x apartine (-infinit,-9)
b)8x+4-6x-4<0 =>> 2x<0 =>> x < 0 =>> x apartine (-infinit,0)
c)2x-6+6x>2 =>> 8x+6 > 2 =>> 8x > -4 =>> x > -4/8 =>> x>-1/2 =>>x apartine (-1/2,infinit)
d)8x-10x+20<10 =>> -2x< -10 =>> x>5 =>> x apartine (5,infinit)
e)9x+4-10x+5<3 =>> -x+9<3 =>> -x<-6 =>> x>6 =>> x apartine (6,infinit)
f)2x-3x-3>x+5 =>> -x-3>x+5 =>>-2x>8 =>> -x>4 =>> x>-4 =>> x apartine (-4,infinit)
g)7x-12-8x>x =>>-x-12>x=>>-2x>12 =>> -x>6 =>> x>-6 =>> x apartine (-6,infinit)
h)2x+3-3x-3<1-x =>>-x<1-x =>>nu exista solutie pentru ca se reduce x-ul