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What is the value of w in the equation 1/2w+7=2w-2

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(1)/(2)w+7=2w-2\ \ \ \ |subtract\ 7\ from\ both\ sides\\\\(1)/(2)w=2w-9\ \ \ \ |subtract\ 2w\ from\ both\ sides\\\\-1(1)/(2)w=-9\\\\-1.5w=-9\ \ \ \ |divide\ both\ sides\ by\ (-1.5)\\\\\boxed{w=6}
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