Question

Solve the following system of equations in R.

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

Answer 1

Consider the first inequation,

$10\le -5(x-2)2\le -(x-2)2\le -x+22-2\le -x0\le -xx\le 0$

Consider the second inequation,

$-5(x-2)<20-5x+10<20-5x<20-10-5x<10-x<2x>-2$

From (i) and (ii),$(-2,0)$ is the solution set of the simultaneous equations.