SAT Question 3f8a701b: Linear Equations In One Variable answer and explanation with Desmos solution

Choice D is correct. For a linear equation in a form $ax+b=cx+d$ to have no solutions, the $x$-terms must have equal coefficients and the remaining terms must not be equal. Expanding the right-hand side of the given equation yields $9x+5=ax+ab$. Inspecting the $x$-terms, $9$ must equal $a$, so statement I must be true. Inspecting the remaining terms, $5$ can't equal $9b$. Dividing both of these quantities by $9$ yields that $b$ can't equal $\frac{5}{9}$. Therefore, statement III must be true. Since $b$ can have any value other than $\frac{5}{9}$, statement II may or may not be true.