Question

ac{1}{2x} | = 3" alt="5 - | \frac{1}{2x} | = 3" align="absmiddle" class="latex-formula">

Answer 1

$\text{The domain:}\ x\neq0\\\\5-\left|\dfrac{1}{2x}\right|=3\qquad\text{Subtract 5 from both sides}\\\\-\left|\dfrac{1}{2x}\right|=-2\qquad\text{change the signs}\\\\\left|\dfrac{1}{2x}\right|=2\iff\dfrac{1}{2x}=2\ \vee\ \dfrac{1}{2x}=-2\\\\\dfrac{1}{2x}=\dfrac{2}{1}\ \vee\ \dfrac{1}{2x}=\dfrac{-2}{1}\qquad\text{cross multiply}\\\\(2)(2x)=(1)(1)\ \vee\ (2x)(-2)=(1)(1)\\\\4x=1\ \vee\ -4x=1\qquad\text{divide both sides by 4, (-4)}\\\\\boxed{x=\dfrac{1}{4}\ \vee\ x=-\dfrac{1}{4}}$