Решить двойные неравенства:
а)
![-2\le 3x+5\le 2\\\\\begin {cases} 3x+5\ge \:-2 \\ 3x+5\le \:2\end. \Rightarrow \:\:\begin {cases} 3x\ge \:-7 \\ 3x\le \:-3\end. \Rightarrow \:\:\begin {cases} x\ge \:-\frac{7}{3} \\ x\le \:-1\end.\\\\\\-\frac{7}{3}\le \:x\le \:-1\\\\x\in \left[-\frac{7}{3},\:-1\right]](https://tex.z-dn.net/?f=-2%5Cle%203x%2B5%5Cle%202%5C%5C%5C%5C%5Cbegin%20%7Bcases%7D%203x%2B5%5Cge%20%5C%3A-2%20%5C%5C%203x%2B5%5Cle%20%5C%3A2%5Cend.%20%5CRightarrow%20%5C%3A%5C%3A%5Cbegin%20%7Bcases%7D%203x%5Cge%20%5C%3A-7%20%5C%5C%203x%5Cle%20%5C%3A-3%5Cend.%20%5CRightarrow%20%5C%3A%5C%3A%5Cbegin%20%7Bcases%7D%20x%5Cge%20%5C%3A-%5Cfrac%7B7%7D%7B3%7D%20%5C%5C%20x%5Cle%20%5C%3A-1%5Cend.%5C%5C%5C%5C%5C%5C-%5Cfrac%7B7%7D%7B3%7D%5Cle%20%5C%3Ax%5Cle%20%5C%3A-1%5C%5C%5C%5Cx%5Cin%20%5Cleft%5B-%5Cfrac%7B7%7D%7B3%7D%2C%5C%3A-1%5Cright%5D "-2\le 3x+5\le 2\\\\\begin {cases} 3x+5\ge \:-2 \\ 3x+5\le \:2\end. \Rightarrow \:\:\begin {cases} 3x\ge \:-7 \\ 3x\le \:-3\end. \Rightarrow \:\:\begin {cases} x\ge \:-\frac{7}{3} \\ x\le \:-1\end.\\\\\\-\frac{7}{3}\le \:x\le \:-1\\\\x\in \left[-\frac{7}{3},\:-1\right]")
б)
\:2x-5 \\ 3x+7\le \:8\end. \Rightarrow \:\:\begin {cases} x > \:-12 \\ 3x\le \:1\end. \Rightarrow \:\:\begin {cases} x > \:-12 \\ x\le \frac{1}{3} \end.\\\\\\-12 \:2x-5 \\ 3x+7\le \:8\end. \Rightarrow \:\:\begin {cases} x > \:-12 \\ 3x\le \:1\end. \Rightarrow \:\:\begin {cases} x > \:-12 \\ x\le \frac{1}{3} \end.\\\\\\-12
в)
г)
![-2,5\le \frac{1-3y}{2}\le 1,5\\\\-5\le 1-3y\le3\\\\\begin {cases} 1-3y \ge \:-5 \\ 1-3y \le \:3\end. \Rightarrow \:\:\begin {cases} -3y \ge \:-6 \\ -3y \le \:2\end. \Rightarrow \:\:\begin {cases} y \le \:2 \\ y \ge -\frac{2}{3} \end.\\\\\\-\frac{2}{3}\le \:y\le \:2\\\\x\in \left[-\frac{2}{3},\:2\right]](https://tex.z-dn.net/?f=-2%2C5%5Cle%20%5Cfrac%7B1-3y%7D%7B2%7D%5Cle%201%2C5%5C%5C%5C%5C-5%5Cle%201-3y%5Cle3%5C%5C%5C%5C%5Cbegin%20%7Bcases%7D%201-3y%20%5Cge%20%5C%3A-5%20%5C%5C%201-3y%20%5Cle%20%5C%3A3%5Cend.%20%5CRightarrow%20%5C%3A%5C%3A%5Cbegin%20%7Bcases%7D%20-3y%20%5Cge%20%5C%3A-6%20%5C%5C%20-3y%20%5Cle%20%5C%3A2%5Cend.%20%5CRightarrow%20%5C%3A%5C%3A%5Cbegin%20%7Bcases%7D%20y%20%5Cle%20%5C%3A2%20%5C%5C%20y%20%5Cge%20-%5Cfrac%7B2%7D%7B3%7D%20%5Cend.%5C%5C%5C%5C%5C%5C-%5Cfrac%7B2%7D%7B3%7D%5Cle%20%5C%3Ay%5Cle%20%5C%3A2%5C%5C%5C%5Cx%5Cin%20%5Cleft%5B-%5Cfrac%7B2%7D%7B3%7D%2C%5C%3A2%5Cright%5D "-2,5\le \frac{1-3y}{2}\le 1,5\\\\-5\le 1-3y\le3\\\\\begin {cases} 1-3y \ge \:-5 \\ 1-3y \le \:3\end. \Rightarrow \:\:\begin {cases} -3y \ge \:-6 \\ -3y \le \:2\end. \Rightarrow \:\:\begin {cases} y \le \:2 \\ y \ge -\frac{2}{3} \end.\\\\\\-\frac{2}{3}\le \:y\le \:2\\\\x\in \left[-\frac{2}{3},\:2\right]")