Question

ex 4 cu tot cu a si b va rog mult dau 25 de punte + coroana + 5 stele si multumesc.

Answer 1

Sper ca te-am ajutat.Coroana?

Answer 2

$\it -5\leq\dfrac{2x+1}{3}<7|_{\cdot3} \Rightarrow-15\leq2x+1<21|_{-1} \Rightarrow -16\leq2x<20|_{:2}\Rightarrow \\ \\ \\ \Rightarrow -8\leq x <10 \Rightarrow A = [-8,\ \ 10) \\ \\ \\ |3x-7|<1 \Rightarrow -1<3x-7<1|+7\Rightarrow 6\leq3x<8|_{:3} \Rightarrow 2\leq x<\dfrac{8}{3}\Rightarrow \\ \\ \\ \Rightarrow B = \left[2,\ \ \dfrac{8}{3}\right)$

$\it\ b) A\cup B = [-8,\ \ 10)\cup \left[2,\ \ \dfrac{8}{3}\right) = [-8,\ \ 10) \\ \\ A\cap B = [-8,\ \ 10)\cap \left[2,\ \ \dfrac{8}{3}\right) = \left[2,\ \ \dfrac{8}{3}\right) \\ \\ \\ A\backslash B = [-8,\ \ 10)\backslash \left[2,\ \ \dfrac{8}{3}\right) = [-8,\ 2)\cup \left[\dfrac{8}{3},\ \ 10\right) \\ \\ \\ C_{\mathbb{R}} B = \mathbb{R}\backslash B = (-\infty,\ \ 2)\cup \left[\dfrac{8}{3},\ \ \infty\right)$