Question

bună seara! ma poate ajuta va rog cineva la acest ex?​

Answer 1

a) 3x+15+2(3x-1)+2x-7<5x+5+9
3x+15+6x-2+2x-7<5x+14
11x+6<5x+14
11x-5x<14-6
6x<8
x<8/6 ; x€N => x={0,1}
b)Cazul 1:x<0, x€Z
5x+10-3(-2x+5)+2x+6>=7x+21-14
5x+10+6x-15+2x+6>=7x+7
13x+1>=7x+7
13x-7x>=7-1
6x>=6
x>=1 => x€[1,infinit)
Cazul 2: x>0, x€Z
5x+10-3(2x+5)+2x+6>=7x+21-14
5x+10-6x-15+2x+6>=7x+7
X+1>=7x+7
X-7x>=7-1
-6x>=6 |*(-1)
6x<=-6
x<=-1 => x€ (-infinit,-1]
Deci x €(-infinit,-1] intersectat cu [1,infinit)
c) Cazul 1: x<0
4x+4-2(-2x+3)-2x-2>2x-4
4x+4+4x-6-2x-2>2x-4
6x-4>2x-4
6x-2x>-4+4
4x>0
x>0 => x€(0, infinit)
Cazul 2: x>0
4x+4-2(2x+3)-2x-2>2x-4
4x+4-4x-6-2x-2>2x-4
-2x-4>2x-4
-2x-2x>-4+4
-4x>0
x>0 => x€(0,infinit)
Deci x apartine la (0,infinit)