Question

Identify each equation has no solution, one solution, or infinitely many solutions -2x + 3 = -3x + 2- 2x + 3 = -2x + 3- 2x + 3 = 2x + 3

Answer 1

For equation 1;

$\begin{gathered} -2x+3=-3x+2 \\ \text{Collect like terms} \\ -2x+3x=2-3 \\ x=-1 \\ \text{This equation has one solution} \end{gathered}$

For equation 2;

$\begin{gathered} -2x+3=-2x+3 \\ \text{Collect like terms} \\ -2x+2x=3-3 \\ 0=0 \\ \text{This equation has infinitely many solutions} \end{gathered}$

For equation 3;

$\begin{gathered} -2x+3=2x+3 \\ \text{Collect like terms} \\ -2x-2x=3-3 \\ -4x=0 \\ \text{Divide both sides by -4} \\ x=0 \\ \text{This equation has only one solution} \end{gathered}$