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Advanced Math Difficulty: Hard

$|x - 9| + 45 = 63$

What is the sum of the solutions to the given equation?

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Explanation

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