Answer
The solution is $\Big(-\dfrac{3}{2},\dfrac{5}{2}\Big)$
Work Step by Step
$\Big|\dfrac{1}{2}-x\Big|\lt2$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-2\lt\dfrac{1}{2}-x\lt2$
Multiply the whole inequality by $-2$:
$-2\Big(-2\lt\dfrac{1}{2}-x\lt2\Big)$
$4\gt-1+2x\gt-4$
Add $1$ to all three parts of the inequality:
$4+1\gt-1+1+2x\gt-4+1$
$5\gt2x\gt-3$
Divide all three parts of the inequality by $2$:
$\dfrac{5}{2}\gt\dfrac{2x}{2}\gt-\dfrac{3}{2}$
$\dfrac{5}{2}\gt x\gt-\dfrac{3}{2}$
Expressing the solution in interval notation:
$\Big(-\dfrac{3}{2},\dfrac{5}{2}\Big)$
