Explicație pas cu pas:
c)
q = - 2,(27)
[tex]n \leqslant q < n + 1 \\ - 3 \leqslant - 2.(27) < - 2 \implies n = - 3[/tex]
-q = 2,(27)
[tex]m \leqslant - q < m + 1 \\ 2 \leqslant 2.(27) < 3 \implies m = 2[/tex]
=> {n} ∪ {m} = {-3; 2}
d)
[tex]q = - 2.(27) = - \frac{227 - 2}{99} = - \frac{225}{99} \\ q = - \frac{25}{11} [/tex]
[tex]2(x + 3) - q > 3x + \frac{3}{11} \\ 2x + 6 + \frac{25}{11} > 3x + \frac{3}{11} \\ \frac{66 + 25}{11} - \frac{3}{11} > 3x - 2x \\ \frac{91 - 3}{11} > x \iff x < \frac{88}{11} \\ \implies x < 8[/tex]
=> x ∈ (- ∞; 8)
