Question

If $|4x-3|=|x+5|$, then $x$ is/are

• A. $\frac{8}{3}$
• B. $-\frac{2}{5}$
• C. $-\frac{8}{3}$
• D. $\frac{2}{5}$

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{8}{3}$
B $-\frac{2}{5}$

$|4x-3|=|x+5|$
$\Rightarrow 4x-3=\pm (x+5)$
$\Rightarrow 4x-3=x+5\text{or}4x-3=-x-5$
$\Rightarrow x=\frac{8}{3}\text{or}x=-\frac{2}{5}$