SAT Question 55ea0659: Linear Equations In One Variable answer and explanation with Desmos solution

Choice D is correct. In the given equation, $x(r-9)+4=19x+27$, $r$ is a positive integer. Distributing on the left-hand side of this equation yields $rx-9x+4=19x+27$. Subtracting $4$ from both sides of this equation yields $rx-9x=19x+23$. Subtracting $19x$ from both sides of this equation yields $rx-28x=23$, which can be written as $(r-28)x=23$. For this equation to have exactly one solution, the coefficient of $x$, $(r-28)$, cannot be equal to $0$. Therefore, $28$ CANNOT be the value of $r$.