#### Answer

set of all real numbers

#### Work Step by Step

The given inequality, $
|x-2|+3\ge2
,$ is equivalent to
\begin{array}{l}\require{cancel}
|x-2|\ge2-3
\\\\
|x-2|\ge-1
.\end{array}
For any $x$, the left side of the inequality above is a nonnegative number. This is always greater than the negative number at the right. Hence, the solution is the $\text{
set of all real numbers
.}$