For choice A, we can rearrange the equation to [tex]38x=0,[/tex] so it has exactly one solution, [tex]x=0.[/tex]
For choice B, we rearrange the equation to [tex]38x=36,[/tex] so this too has exactly one solution, [tex]x=\frac{36}{38}=\frac{18}{19}.[/tex]
Rearranging the equation in choice C by eliminating the [tex]x[/tex] terms gives us the false equality [tex]-18=18,[/tex] so this equation has no solutions.
Eliminating [tex]x[/tex] in the equation in choice D gives the equality [tex]18=18,[/tex] which is always true, so this equation has infinitely many solutions.
Thus, we conclude that choices A and B work.
