Question

Solve each of the following system of equations in R.

24. $\frac{\left|x-2\right|}{x-2}>0$

Answer 1

$$\begin{gathered} \mathrm{We}have,\frac{\left|x-2\right|}{x-2}>0 \\ \mathrm{Clearly},\mathrm{LHS}\mathrm{of}\mathrm{the}\mathrm{inequation}\mathrm{is}\mathrm{meaningful}\mathrm{if}x\ne 2.\left(\mathrm{If}x=2\mathrm{then}\mathrm{denominator}\mathrm{will}\mathrm{become}\mathrm{zero}\right) \\ \mathrm{The}\mathrm{numerator}\mathrm{of}\mathrm{the}\mathrm{LHS}\mathrm{is}\mathrm{positive},\mathrm{so}\mathrm{its}\mathrm{denominator}\mathrm{must}\mathrm{also}\mathrm{be}\mathrm{positive}\mathrm{to}\mathrm{make}\mathrm{the}\mathrm{fraction}\mathrm{positive}. \\ \mathit{\therefore }\mathit{}x>2 \\ \mathit{\therefore }\mathit{}x\in \left(2,\infty \right) \end{gathered}$$