Answer :

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

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