5 + 3x < 5x + 2
Collect like terms
3x - 5x < 2 - 5
- 2x < - 3
When you divide an inequality equation by a negative coefficient, the sign of the inequality changes. I.e '<' change to '>' and '>' change to '<'.
Therefore,
[tex]\begin{gathered} \frac{-2x}{-2}\text{ > }\frac{-3}{-2} \\ x\text{ >}\frac{3}{2} \end{gathered}[/tex]