Question

Rezolvati in Z inecuatiile:

a)3x+9≥3(x+1)+6
b)5x+3≤2(2x-7)+x+17
c)5(x+1)<5(x-1)+10
d)3(x+2)<3(x-1)+9
e)2x(x-6)+9≥x(x-6)
f)2x(x+5)+16≥x(x+2)
g)(x+2)(x-2)>10x-29
h)(x-3)(x+3)>2(x-5)

Answer 1

a)3x+9>sau egal3(x+1)+6



3x+9>sau egal 3x+3+6
3x+9>sau egal 3x+9- adevarata
b)5x+3<sau egal2(2x-7)+x+17
5x+3<sau egal4x-14+x+17
5x+3<sau egal5x+3-adevarata
c)5(x+1)<5(x-1)+19
5x+5<5x-5+19
5x+5<5x+14 -adevarata
d)3(x+2)<3(x-1)+9
3x+6<3x-3+9
3x+6<3x+6 -falsa
e)2x(x-6)+9>sau egalx(x-6)
2xla puterea a doua-12x+9>sau egalx la puterea a doua-6x -adevarata
f)2x(x+5)+16>sau egalx(x+2)
2xla puterea a doua+10x+16>sau egal cu la puterea a doua+2x - adevărată

g)(x+2)(x-2)>10x-29
xla puterea a doua-2x+2x-4>10x-29
xla p.a doua-4>10x-29 adevărat
h)(x-3)(x+3)>2(x-5)
xla puterea a doua+3x-3x-9>2x-10
xla puterea a doua-9>2x-10 adevarata