Question

Solve each of the following system of equations in R.

19. 10 ≤ −5 (x − 2) < 20

Answer 1

$$\begin{gathered} 10\le -5\left(x-2\right)<20 \\ \Rightarrow 10\le -5x+10<20 \\ \Rightarrow 10-10\le -5x<20-10(\mathrm{Substracting}10\mathrm{from}\mathrm{all}\mathrm{three}\mathrm{terms}) \\ \Rightarrow 0\le -5x<10 \\ \Rightarrow 0\ge x>-2(\mathrm{Dividing}\mathrm{all}\mathrm{three}\mathrm{terms}\mathrm{by}-5) \\ \Rightarrow x\in (-2,0] \end{gathered}$$

Hence, the interval (-2,0] is the solution of the given set of inequations.