Solve each of the following system of equations in R. 19. 10 ≤ −5 (x − 2) < 20
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.