[tex]-\frac{x}{2}+\frac{3}{2}<\frac{5}{2}[/tex]
Subtracting 3/2 at both sides of the inequality:
[tex]\begin{gathered} -\frac{x}{2}+\frac{3}{2}-\frac{3}{2}<\frac{5}{2}-\frac{3}{2} \\ -\frac{x}{2}<1 \end{gathered}[/tex]
Multiplying by 2 at both sides of the inequality:
[tex]\begin{gathered} -\frac{x}{2}\cdot2<1\cdot2 \\ -x<2 \end{gathered}[/tex]
Dividing by -1 at both sides of the inequality:
[tex]\begin{gathered} \frac{-x}{-1}<\frac{2}{-1} \\ x>-2 \end{gathered}[/tex]
(Dividing by a negative number changes the inequality symbol)
This solution is represented on the number line as follows:
Notice that -2 is not included in the solution.
