Question

Solve each of the following system of equations in R.

 10 ≤ −5 (x − 2) < 20 

Answer 1

$$10\le -5(x-2)<20$$

$$\Rightarrow 10\le -5x+10<20$$

$$\Rightarrow 10-10\le -5x<20-10(\text{ Substracting 10 from all three terms })$$

$$\Rightarrow 0\le -5x<10$$

$$\Rightarrow 0\ge x>-2(\text{ Dividing all three terms by }-5)$$

$$\Rightarrow x\in (-2,0]$$

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