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Simplifying 1194 = 2(27) * w + 2(27)(12) + 2(w)(12) Multiply 2 * 27 1194 = 54w + 2(27)(12) + 2(w)(12) Multiply 2 * 27 1194 = 54w + 54 * 12 + 2(w)(12) Multiply 54 * 12 1194 = 54w + 648 + 2(w)(12) Reorder the terms for easier multiplication: 1194 = 54w + 648 + 2 * 12w Multiply 2 * 12 1194 = 54w + 648 + 24w Reorder the terms: 1194 = 648 + 54w + 24w Combine like terms: 54w + 24w = 78w 1194 = 648 + 78w Solving 1194 = 648 + 78w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-78w' to each side of the equation. 1194 + -78w = 648 + 78w + -78w Combine like terms: 78w + -78w = 0 1194 + -78w = 648 + 0 1194 + -78w = 648 Add '-1194' to each side of the equation. 1194 + -1194 + -78w = 648 + -1194 Combine like terms: 1194 + -1194 = 0 0 + -78w = 648 + -1194 -78w = 648 + -1194 Combine like terms: 648 + -1194 = -546 -78w = -546 Divide each side by '-78'. w = 7 Simplifying w = 7
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