Question

The general solution of the inequality $-9\le 1-2(x+3)<1$ and $-5\le \frac{x-9}{2}\le 8$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$-9\le 1-2(x+3)<1$
$\Rightarrow -10\le -2(x+3)<0$
$\Rightarrow -5\le -(x+3)<0$
$\Rightarrow 0\le x+3\le 5$
$\Rightarrow -3<x\le \mathrm{2...}\left(1\right)$

Now,
$-5\le \frac{x-9}{2}\le 8$
$\Rightarrow -10\le x-9\le 16$
$\Rightarrow -1\le x\le \mathrm{25...}\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$
$$=$$