Question

Am nevoie de exercițiul 11 !!!Va rog !!!

Answer 1

Explicație pas cu pas:

11.a)

$1 < x < 7$

x ∈ N => A = {2, 3, 4, 5, 6}

cardA = 5

b)

$|x + 1| < 5 \\ - 5 < x + 1 < 5 \\ - 5 - 1 < x < 5 - 1 \\ - 6 < x < 4$

x ∈ N* => A = {1, 2, 3}

cardA = 3

c)

$| \frac{x - 7}{2} | < 1 \\ - 1 < \frac{x - 7}{2} < 1 \\ - 2 < x - 7 < 2 \\ - 2 + 7 < x < 2 + 7 \\ 5 < x < 9$

x ∈ Z => A = {6, 7, 8}

cardA = 3

d)

$|2x + 1| \leqslant 7 \\ - 7 \leqslant 2x + 1 \leqslant 7 \\ - 8 \leqslant 2x \leqslant 6 \\ - 4 \leqslant x \leqslant 3$

x ∈ Z => A = {-4, -3, -2, -1, 0, 1, 2, 3}

cardA = 8

e)

$|x - 3| < 5 \\ - 5 < x - 3 < 5 \\ - 5 + 3 < x < 5 + 3 \\ - 2 < x < 8$

x ∈ Z* => A = {-1, 1, 2, 3, 4, 5, 6, 7}

cardA = 8

f)

$- 7 < 3x + 5 < 11 \\ - 7 - 5 < 3x < 11 - 5 \\ - 12 < 3x < 6 \\ - 12 \div 3 < x < 6 \div 3 \\ - 4 \leqslant x \leqslant 2$

x ∈ Z* => A = {-4, -3, -2, -1, 1, 2}

cardA = 6