SAT Question c7789423: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

By the definition of absolute value, if $\left|x-2\right|=9$, then $x-2=9$ or $x-2=-9$. Adding $2$ to both sides of the equation $x-2=9$ yields $x=11$. Adding $2$ to both sides of the equation $x-2=-9$ yields $x=-7$. Thus, the given equation, $\left|x-2\right|=9$, has two possible solutions, $11$ and $-7$. Note that 11 and -7 are examples of ways to enter a correct answer.