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Simplifying x(y + 40) = (x + 10)(y + 20) Reorder the terms: x(40 + y) = (x + 10)(y + 20) (40 * x + y * x) = (x + 10)(y + 20) (40x + xy) = (x + 10)(y + 20) Reorder the terms: 40x + xy = (10 + x)(y + 20) Reorder the terms: 40x + xy = (10 + x)(20 + y) Multiply (10 + x) * (20 + y) 40x + xy = (10(20 + y) + x(20 + y)) 40x + xy = ((20 * 10 + y * 10) + x(20 + y)) 40x + xy = ((200 + 10y) + x(20 + y)) 40x + xy = (200 + 10y + (20 * x + y * x)) 40x + xy = (200 + 10y + (20x + xy)) Reorder the terms: 40x + xy = (200 + 20x + xy + 10y) 40x + xy = (200 + 20x + xy + 10y) Add '-1xy' to each side of the equation. 40x + xy + -1xy = 200 + 20x + xy + -1xy + 10y Combine like terms: xy + -1xy = 0 40x + 0 = 200 + 20x + xy + -1xy + 10y 40x = 200 + 20x + xy + -1xy + 10y Combine like terms: xy + -1xy = 0 40x = 200 + 20x + 0 + 10y 40x = 200 + 20x + 10y Solving 40x = 200 + 20x + 10y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20x' to each side of the equation. 40x + -20x = 200 + 20x + -20x + 10y Combine like terms: 40x + -20x = 20x 20x = 200 + 20x + -20x + 10y Combine like terms: 20x + -20x = 0 20x = 200 + 0 + 10y 20x = 200 + 10y Divide each side by '20'. x = 10 + 0.5y Simplifying x = 10 + 0.5y
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