SAT Question c9417793: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Subtracting $45$ from each side of the given equation yields $\left|x-9\right|=18$. By the definition of absolute value, if $\left|x-9\right|=18$, then $x-9=18$ or $x-9=-18$. Adding $9$ to each side of the equation $x-9=18$ yields $x=27$. Adding $9$ to each side of the equation $x-9=-18$ yields $x=-9$. Therefore, the solutions to the given equation are $27$ and $-9$, and it follows that the sum of the solutions to the given equation is $27+\left(-9\right)$, or $18$.