Question

If $\frac{|x+2|}{|x-4|}=3$, then the value(s) of $x$ is/are

• A. $\frac{5}{2}$
• B. $\frac{7}{2}$
• C. $7$
• D. $9$

Answer 1

Answer: (A), (C)

The correct options are
A $\frac{5}{2}$
C $7$

$\frac{|x+2|}{|x-4|}=3$
$\Rightarrow \left|\frac{x+2}{x-4}\right|=3$
$(\because \frac{|a|}{|b|}=\left|\frac{a}{b}\right|)$
$\Rightarrow \frac{x+2}{x-4}=\pm 3$

Case 1:
$\Rightarrow \frac{x+2}{x-4}=3$
$\Rightarrow x+2=3(x-4)$
$\Rightarrow 2x=14$
$\Rightarrow x=7$

Case 2:
$\Rightarrow \frac{x+2}{x-4}=-3$
$\Rightarrow x+2=-3(x-4)$
$\Rightarrow 4x=10$
$\Rightarrow x=\frac{5}{2}$