x - 9 + 45 = 63 What is the sum of the solutions to the

The correct answer is $18$. 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 $18$.