ANSWER
0 < x < 4
EXPLANATION
To solve this inequality, first, we have to add 3 to all sides,
[tex]\begin{gathered} -3+3\lt2x-3+3\lt5+3 \\ \\ 0\lt2x\lt8 \end{gathered}[/tex]And then, divide by 2,
[tex]\begin{gathered} \frac{0}{2}\lt\frac{2x}{2}\lt\frac{8}{2} \\ \\ 0\lt x\lt4 \end{gathered}[/tex]Hence, the set of solutions is 0 < x < 4.
