Question

Dau 50 puncte! Am nevoie de ex 15 punctele c,B,d!! Va rog !! Am mare nevoie

Answer 1

In acest exercitiu ai de incadrat relatia necunoscuta in semnele conform intervalului respectiv

b) 3x-1 apartine (-5, 7)  adica

-5 < 3x-1 < 7   aduni toata inecuatia cu 1

-5+1 < 3x-1+1 < 7+1

-4 < 3x < 8   imparti toata inecuatia cu 3

-4/3 < 3x/3 < 8/3

Deci A = (-4/3, 8/3)

c) 2x+5 apartine (-7, 3)

-7 < 2x+5 < 3 scazi inecuatia cu 5

-12 < 2x < -2  imparti cu 2

-6 < x < -1

Deci A = (-6, -1)

d) (2x+1)/3 apartine (-3, 5]

-3 < (2x+1)/3 </ 5  amplifici pe -3 si pe 5 cu 3 ca sa scapi de numitor

-9 < 2x+1 </ 15  scazi cu 1

-10 < 2x </ 14  imparti cu 2

-5 < x </ 7

Deci A = (-5, 7]

Answer 2

Explicație pas cu pas:

15.

b)

$- 5 < 3x - 1 < 7 \ \ \Big| + 1 \\ - 4 < 3x < 8 \ \ \Big| : 3 \\ - \frac{4}{3} < x < \frac{8}{3}$

$A = \Big( - \frac{4}{3} ; \frac{8}{3} \Big)$

c)

$- 7 < 2x + 5 < 3 \ \ \Big| - 5 \\ - 12 < 2x < - 2 \ \ \Big| : 2 \\ - 6 < x < - 1$

$A = \Big( - 6 ; - 1\Big)$

d)

$- 3 < \frac{2x + 1}{3} \leqslant 5 \ \ \Big| \times 3 \\ - 9 < 2x + 1 \leqslant 15 \ \ \Big| - 1 \\ - 10 < 2x \leqslant 14 \ \ \Big| : 2 \\ - 5 < x \leqslant 7$

$A = \Big( - 5 ; 7\Big]$

e)

$- 1 \leqslant \frac{2x + 7}{5} < 5 \ \ \Big| \times 5 \\ - 5 \leqslant 2x + 7 < 25 \ \ \Big| - 7 \\ - 12 \leqslant 2x < 18 \ \ \Big| : 2 \\ - 6 \leqslant x < 9$

$A = \Big[ - 6 ; 9\Big)$