For equation 1;
[tex]\begin{gathered} -2x+3=-3x+2 \\ \text{Collect like terms} \\ -2x+3x=2-3 \\ x=-1 \\ \text{This equation has one solution} \end{gathered}[/tex]For equation 2;
[tex]\begin{gathered} -2x+3=-2x+3 \\ \text{Collect like terms} \\ -2x+2x=3-3 \\ 0=0 \\ \text{This equation has infinitely many solutions} \end{gathered}[/tex]For equation 3;
[tex]\begin{gathered} -2x+3=2x+3 \\ \text{Collect like terms} \\ -2x-2x=3-3 \\ -4x=0 \\ \text{Divide both sides by -4} \\ x=0 \\ \text{This equation has only one solution} \end{gathered}[/tex]