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Simplifying 6x + -3y + 12w + -6y + -5w + 8x = 0 Reorder the terms: 12w + -5w + 6x + 8x + -3y + -6y = 0 Combine like terms: 12w + -5w = 7w 7w + 6x + 8x + -3y + -6y = 0 Combine like terms: 6x + 8x = 14x 7w + 14x + -3y + -6y = 0 Combine like terms: -3y + -6y = -9y 7w + 14x + -9y = 0 Solving 7w + 14x + -9y = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-14x' to each side of the equation. 7w + 14x + -14x + -9y = 0 + -14x Combine like terms: 14x + -14x = 0 7w + 0 + -9y = 0 + -14x 7w + -9y = 0 + -14x Remove the zero: 7w + -9y = -14x Add '9y' to each side of the equation. 7w + -9y + 9y = -14x + 9y Combine like terms: -9y + 9y = 0 7w + 0 = -14x + 9y 7w = -14x + 9y Divide each side by '7'. w = -2x + 1.285714286y Simplifying w = -2x + 1.285714286y
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