all real numbers
Work Step by Step
The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from $0,$ and hence, is always a nonnegative number. Therefore, the left side of the given inequality, $ |2y-9|\gt-5 ,$ is always nonnegative. This is always greater than the negative value at the right. Hence, the solution is the set of all real numbers.