Question

Solve the following set of inequations:-
x-2/x+2 ≥3, 2x-7 ≤ 5

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \frac{\mathrm{x}-2}{\mathrm{x}+2}\ge 3 \\ \frac{\mathrm{x}-2}{\mathrm{x}+2}-3\ge 0\mathrm{or}\frac{\mathrm{x}-2-3\mathrm{x}-6}{\mathrm{x}+2}\ge 0 \\ \frac{\mathrm{x}+4}{\mathrm{x}+2}\le 0 \\ \mathrm{x}\in \left[-4,-2\right]....\left[1\right] \\ \mathrm{Also}, \\ 2\mathrm{x}-7\le 5 \\ 2\mathrm{x}-12\le 0 \\ \mathrm{x}-6\le 0 \\ \mathrm{x}\in (-\infty ,6].......\left[2\right] \\ \mathrm{Now}\mathrm{common}\mathrm{solution}\mathrm{of}\mathrm{equation}1\mathrm{and}2\mathrm{is} \\ \mathrm{x}\in \left[-4,-2\right] \\ \mathrm{Regards} \end{gathered}$$