Question

For any positive real number 'a', the following results hold.
(i) $\left|x\right|\le a\Rightarrow -a\le x\le a$
(ii) $\left|x\right|\ge a\Rightarrow x\ge a$ or $x\le a$
Using the above indentities, evaluate the following:

$\left|\frac{4m-8}{2}\right|\le 6$

• A. $1\le m\le 5$
• B. $-1\le m\le 5$
• C. $1\le m\le -5$
• D. $-1\le m\le -5$

Answer 1

The correct option is B $-1\le m\le 5$

$|\frac{4m-8}{2}|\le 6$
$-6\le \frac{4m-8}{2}\le 6$
$-6\le 2m-4\le 6$
Adding 4 we get
$-2\le 2m\le 10$
$-1\le m\le 5$
Hence answer is B