[tex] \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) [/tex]
[tex] \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) [/tex]
