Answer
$(-∞,∞)$
Work Step by Step
We are given the inequality $|5x-8|+9\geq7$. In order to solve, first subtract 9 from both sides.
$|5x-8|\geq-2$
Therefore, $x$ will have a solution of all real numbers, because the absolute value of $5x-8$ will be greater than -2 for all real numbers.