#### Answer

$\left( -\dfrac{3}{2},\dfrac{5}{2}\right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\left|\dfrac{1}{2}-x \right|\lt2
,$ remove the absolute value sign using the properties of absolute value inequality. Then use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
For any $a\gt0,$ $|x|\le a$ implies $-a\le x\le a.$ (Note that the symbol $\le$ may be replaced with $\lt.$) Hence, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2\lt \dfrac{1}{2}-x \lt2
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
2(-2)\lt 2\left(\dfrac{1}{2}-x\right) \lt2(2)
\\\\
-4\lt 1-2x\lt4
\\\\
-4-1\lt 1-1-2x\lt4-1
\\\\
-5\lt -2x\lt3
.\end{array}
Dividing both sides by $
-2
$ and reversing the inequality symbols, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-5}{-2}\gt \dfrac{-2x}{-2}\gt\dfrac{3}{-2}
\\\\
\dfrac{5}{2}\gt x\gt-\dfrac{3}{2}
\\\\
-\dfrac{3}{2}\lt x\lt\dfrac{5}{2}
.\end{array}
Hence, the solution is the interval $
\left( -\dfrac{3}{2},\dfrac{5}{2}\right)
.$