Answer
The solution set is $(8, \infty)$
Work Step by Step
The idea is to isolate x on one side.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
---
$ 7-\displaystyle \frac{4}{5}x \lt \frac{3}{5}\qquad $ ... $/\times 5$
$ 35-4x \lt 3\qquad $ ... $/-35$
$-4x \lt -32\qquad $ ... $/\div(-4)$ ... (neagative: change direction)
$ x \gt 8$
The solution set is $(8, \infty)$
