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Simplifying 7x + -2y + 12w + 6y + -3w + 5x = 0 Reorder the terms: 12w + -3w + 7x + 5x + -2y + 6y = 0 Combine like terms: 12w + -3w = 9w 9w + 7x + 5x + -2y + 6y = 0 Combine like terms: 7x + 5x = 12x 9w + 12x + -2y + 6y = 0 Combine like terms: -2y + 6y = 4y 9w + 12x + 4y = 0 Solving 9w + 12x + 4y = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12x' to each side of the equation. 9w + 12x + -12x + 4y = 0 + -12x Combine like terms: 12x + -12x = 0 9w + 0 + 4y = 0 + -12x 9w + 4y = 0 + -12x Remove the zero: 9w + 4y = -12x Add '-4y' to each side of the equation. 9w + 4y + -4y = -12x + -4y Combine like terms: 4y + -4y = 0 9w + 0 = -12x + -4y 9w = -12x + -4y Divide each side by '9'. w = -1.333333333x + -0.4444444444y Simplifying w = -1.333333333x + -0.4444444444y
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