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Simplifying 6x + -2y + 12w + 7y + -3w + 5x = 0 Reorder the terms: 12w + -3w + 6x + 5x + -2y + 7y = 0 Combine like terms: 12w + -3w = 9w 9w + 6x + 5x + -2y + 7y = 0 Combine like terms: 6x + 5x = 11x 9w + 11x + -2y + 7y = 0 Combine like terms: -2y + 7y = 5y 9w + 11x + 5y = 0 Solving 9w + 11x + 5y = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11x' to each side of the equation. 9w + 11x + -11x + 5y = 0 + -11x Combine like terms: 11x + -11x = 0 9w + 0 + 5y = 0 + -11x 9w + 5y = 0 + -11x Remove the zero: 9w + 5y = -11x Add '-5y' to each side of the equation. 9w + 5y + -5y = -11x + -5y Combine like terms: 5y + -5y = 0 9w + 0 = -11x + -5y 9w = -11x + -5y Divide each side by '9'. w = -1.222222222x + -0.5555555556y Simplifying w = -1.222222222x + -0.5555555556y
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