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Simplifying 3(x + 7y) + -5(x + 7y) + 9(2x + -2y) = 0 (x * 3 + 7y * 3) + -5(x + 7y) + 9(2x + -2y) = 0 (3x + 21y) + -5(x + 7y) + 9(2x + -2y) = 0 3x + 21y + (x * -5 + 7y * -5) + 9(2x + -2y) = 0 3x + 21y + (-5x + -35y) + 9(2x + -2y) = 0 3x + 21y + -5x + -35y + (2x * 9 + -2y * 9) = 0 3x + 21y + -5x + -35y + (18x + -18y) = 0 Reorder the terms: 3x + -5x + 18x + 21y + -35y + -18y = 0 Combine like terms: 3x + -5x = -2x -2x + 18x + 21y + -35y + -18y = 0 Combine like terms: -2x + 18x = 16x 16x + 21y + -35y + -18y = 0 Combine like terms: 21y + -35y = -14y 16x + -14y + -18y = 0 Combine like terms: -14y + -18y = -32y 16x + -32y = 0 Solving 16x + -32y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32y' to each side of the equation. 16x + -32y + 32y = 0 + 32y Combine like terms: -32y + 32y = 0 16x + 0 = 0 + 32y 16x = 0 + 32y Remove the zero: 16x = 32y Divide each side by '16'. x = 2y Simplifying x = 2y
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