Answer
$x$ ranges from negative infinity to positive infinity
Work Step by Step
We simplify as follows:
$5+|x-1|\gt\frac{1}{2}$
$|x-1|\gt-\frac{9}{2}$
We know that $|x-1|$ is always a non-negative value, so $|x-1|$ is always greater than $-\frac{9}{2}$
Therefore $x$ can equal anything ($x$ ranges from negative infinity to positive infinity)
