## Intermediate Algebra (12th Edition)

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 $\text{ set of all real numbers .}$