Step 1:
The given inequalities is $5x-3 < 7$
Adding same quantity +3 to both sides $=> 5x-3+3 < 7+3$
=> $ 5x <10$
Dividing by same positive quantities on both sides,
=> $ \large\frac{5x}{5} < \frac{10}{5}$
=> $ x < 2$
Step 2:
The integer less than 2 are ,
$...........-5,-4,-3,,-2,-1,0,1$
The solution set is ,
$\{ ....,-5,-4,-3,-2,-1,0,1\}$
Step 3:
when x is a real number all real number less than 2 satisfy the inequality .
The solution set is $ x \in (- \infty ,2)$