SAT Question 3a01a5ee: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. By the definition of absolute value, if $\left|-5x+13\right|=73$, then $-5x+13=73$ or $-5x+13=-73$. Subtracting $13$ from both sides of the equation $-5x+13=73$ yields $-5x=60$. Dividing both sides of this equation by $-5$ yields $x=-12$. Subtracting $13$ from both sides of the equation $-5x+13=-73$ yields $-5x=-86$. Dividing both sides of this equation by $-5$ yields $x=\frac{86}{5}$. Therefore, the solutions to the given equation are $-12$ and $\frac{86}{5}$, and it follows that the sum of the solutions to the given equation is $-12+\frac{86}{5}$, or $\frac{26}{5}$.