Answer
set of all real numbers
Work Step by Step
The given inequality, $
|x-4|+5\ge4
,$ is equivalent to
\begin{array}{l}\require{cancel}
|x-4|\ge4-5
\\\\
|x-4|\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 $\text{
set of all real numbers
.}$
