Question:
Solve each of the following system of equations in R.
19. 10 ≤ −5 (x − 2) < 20
Solution:
$10 \leq-5(x-2)<20$
$\Rightarrow 10 \leq-5 x+10<20$
$\Rightarrow 10-10 \leq-5 x<20-10 \quad$ (Substracting 10 from all three terms)
$\Rightarrow 0 \leq-5 x<10$
$\Rightarrow 0 \geq x>-2 \quad$ (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.