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Simplifying 5x + -2y + 12w + 7y + -2w + 7x = 0 Reorder the terms: 12w + -2w + 5x + 7x + -2y + 7y = 0 Combine like terms: 12w + -2w = 10w 10w + 5x + 7x + -2y + 7y = 0 Combine like terms: 5x + 7x = 12x 10w + 12x + -2y + 7y = 0 Combine like terms: -2y + 7y = 5y 10w + 12x + 5y = 0 Solving 10w + 12x + 5y = 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. 10w + 12x + -12x + 5y = 0 + -12x Combine like terms: 12x + -12x = 0 10w + 0 + 5y = 0 + -12x 10w + 5y = 0 + -12x Remove the zero: 10w + 5y = -12x Add '-5y' to each side of the equation. 10w + 5y + -5y = -12x + -5y Combine like terms: 5y + -5y = 0 10w + 0 = -12x + -5y 10w = -12x + -5y Divide each side by '10'. w = -1.2x + -0.5y Simplifying w = -1.2x + -0.5y
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