Question

Vă rog frumos să mă ajutați! exercițiile 14 și 15 măcar 5 subpuncte de fiecare exercițiu.

Answer 1

14)

a)3x+9≥3(x+1)+6

3x+9≥3x+3+6

3x+9≥3x+9

9≥9

Număr infinit de soluții.

b)5x+3≤2(2x-7)+x+17

5x+3≤4x-14+x+17

5x+3≤5x+3

3≤3

Număr infinit de soluții.

c)5(x+1)<5(x-1)+10

5x+5<5x-5+10

5x+5<5x+5

Nu are soluții.

d)3(x+2)<3(x-1)+9

3x+6<3x-3+9

3x+6<3x+6

Nu are soluții.

e)2x(x-6)+9≥x(x-6)

2x²-12x+9≥x²-6x

2x²-12x+9=x²-6x

2x²-12x+9-(x²-6x)=x²-6x-(x²-6x)

x²-6x+9=0

(x-3)(x-3)=0

x-3=0=>x=3

x≤3

x≥3

f)2x(x+5)+16≥x(x+2)

2x²+10x+16≥x²+2x

2x²+10x+16-x²+2x≥0

x²+8x+16≥0

(x+4)²≥0

x+4≥0

x≥-4

g)(x+2)(x-2)>10x-29

x²-4>10x-29

x²-4=10x-29

x²-4-(10x-29)=10x-29-(10x-29)

x²-10x+25=0

(x-5)(x-5)=0

x-5=0=>x=5

x<5

x>5

15)

8(1-x)+7x-10<2(7-x)

8-8x+7x-10<14-2x

-2-x<14-2x

-x<14-2x+2

-x<-2x+16

-x+2x<16

x<16

b)2(x+5)+15-9>6(2x+1)

2(x+5)+6>6(2x+1)

2x+10+6>12x+6

2x+12>12x+6

16>12x+6-2x

16>10x+6

16-6>10x

10>10x

1>x

x<1

c)1-7x-2(x-1)+3x≥5(3-x)

1-4x-2(x-1)≥5(3-x)

1-4x-2x+2≥15-5x

3-6x≥15-5x

-6x≥15-5x-3

-6x≥-5x+12

-6x+5x≥12

-x≥12

x≤-12

d)4(x+5)+6(2-x)≤3x-8

4x+20+12-6x≤3x-8

-2x+32≤3x-8

32≤3x-8+2x

32≤5x-8

32+8≤5x

40≤5x

$\frac{40}{5}$≤x

8≤x

x≥8

e)4x+6(x+2)≥36+2(2x+3)

4x+6x+12≥36+4x+6

10x+12≥4x+42

10x≥4x+42-12

10x≥4x+30

10x-4x≥30

6x≥30

x≥$\frac{30}{6}$

x≥5

f)9x+34-3(3x+2)>3(2x+3)

9x+34-9x+6>6x+9

28>6x+9

28-9>6x

19>6x

$\frac{19}{6} > x \\ \\ x < \frac{19}{6}$