Nonlinear equations in one variable and systems of equations in two variables SAT question

The correct answer is $15$ or $-5$. By the definition of absolute value, if $|x-5|=10$, then $x-5=10$ or $x-5=-10$. Adding $5$ to both sides of the first equation yields $x=15$. Adding $5$ to both sides of the second equation yields $x=-5$. Thus, the given equation has two possible solutions, $15$ and $-5$. Note that 15 and -5 are examples of ways to enter a correct answer.