Question

For any positive real number 'a', the following results hold.

(i) $|x|\le a\Rightarrow -a\le x\le a$

(ii) $|x|\ge a\Rightarrow x\ge a$ or $x\le -a$.

Using the above identities, 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 $-1\le m\le 5$

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

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

$\frac{4m-8}{2}\times 2\le 6\times 2$

$\Rightarrow 4m-8\le 12$

$4m-8+8\le 12+8$

$\Rightarrow 4m\le 20$

$m\le 5$

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

$\Rightarrow \frac{4m-8}{2}\ge -6$

Multiply by 2 both sides we get

$\frac{4m-8}{2}\times 2\ge -6\times 2$

$\Rightarrow 4m-8\ge -12$

Add 8 both sides we get

$4m-8+8\ge -12+8$

$\Rightarrow 4m\ge -4$

$\Rightarrow m\ge -1$

So $-1\le m\le 5$