2 4 - x + 3 4 - x = 25 What is the positive solution to the given equation?

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Accepted Answer

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 - 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 - 1 yields x = 9 . Therefore, since the two solutions to the given equation are - 1 and 9 , the positive solution to the given equation is 9 .

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