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Advanced Math Difficulty: Hard

$2 |4 - x| + 3 |4 - x| = 25$

What is the positive solution to the given equation?

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Explanation

The correct answer is $9$ . The given equation can be rewritten as $5 |4 - x| = 25$ . Dividing each side of this equation by $5$ yields $|4 - x| = 5$ . By the definition of absolute value, if $|4 - x| = 5$ , then $4 - x = 5$ or $4 - x = - 5$ . Subtracting $4$ from each side of the equation $4 - x = 5$ yields $- x = 1$ . Dividing each side of this equation by $negative 1$ yields $x = - 1$ . Similarly, subtracting $4$ from each side of the equation $4 - x = - 5$ yields $- x = - 9$ . Dividing each side of this equation by $negative 1$ yields $x equals 9$ . Therefore, since the two solutions to the given equation are $negative 1$ and $9$ , the positive solution to the given equation is $9$ .