Question

2. Scrieţi sub formă de intervale mulţimile:
a) A = {x € R| √√(2x+3)² ≤9};
xa 2||2x+7| <3} ;
5
c)A= {xe R|
b) A = {xe R| √√(2x-7)² <3};
d) A = xe R
= {x
≤3.-)
2x+3
7

Answer 1

Explicație pas cu pas:

12.a)

$|2x + 3| \leqslant 9$

$- 9 \leqslant 2x + 3 \leqslant 9 \\ - 12 \leqslant 2x \leqslant 6 \\ - 6 \leqslant x \leqslant 3$

=> A = [-6; 3]

b)

$|2x - 7| < 3$

$- 3 < 2x - 7 < 3 \\ 4 < 2x < 10 \\ 2 < x < 5$

=> A = (2; 5)

c)

$\Big| \frac{2x + 7}{5} \Big| < 3$

$- 3 < \frac{2x + 7}{5} < 3 \\ - 15 < 2x + 7 < 15 \\ - 22 < 2x < 8 \\ - 11 < x < 4$

=> A = (-11; 4)

d)

$\Big| \frac{2x + 3}{7} \Big| \leqslant 3$

$- 3 \leqslant \frac{2x + 3}{7} \leqslant 3 \\ - 21 \leqslant 2x + 3 \leqslant 21 \\ - 24 \leqslant 2x \leqslant 18 \\ - 12 \leqslant x \leqslant 9$

=> A = [-12; 9]