SAT Question 9a1f1941: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. It's given that $\left|4x-3\right|=-9$. By the definition of absolute value, the left-hand side of this equation, $\left|4x-3\right|$, must be nonnegative. Since the right-hand side of this equation, $-9$, is negative, it follows that no value of $x$ can make this equation true; therefore, the given equation has zero solutions.