We need to solve for x in the equation 1/2(x-2) = 8 + 5/2*(2-x). First, let's simplify the equation: 1/2(x-2) = 8 + 5/2*(2-x) Multiply both sides by 2 to remove the fraction: 2 * 1/2(x-2) = 2 * (8 + 5/2*(2-x)) Simplifying further: (x-2) = 16 + 5*(2-x) Expand the multiplication: x - 2 = 16 + 10 - 5x Combine like terms: 6x - 2 = 26 Add 2 to both sides: 6x = 28 Divide both sides by 6: x = 28/6 Simplifying the fraction: x = 14/3 Therefore, the solution to the equation is x = 14/3 or approximately 4.67.

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