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Simplifying x(y + 40) = (x + 20)(y + 10) Reorder the terms: x(40 + y) = (x + 20)(y + 10) (40 * x + y * x) = (x + 20)(y + 10) (40x + xy) = (x + 20)(y + 10) Reorder the terms: 40x + xy = (20 + x)(y + 10) Reorder the terms: 40x + xy = (20 + x)(10 + y) Multiply (20 + x) * (10 + y) 40x + xy = (20(10 + y) + x(10 + y)) 40x + xy = ((10 * 20 + y * 20) + x(10 + y)) 40x + xy = ((200 + 20y) + x(10 + y)) 40x + xy = (200 + 20y + (10 * x + y * x)) 40x + xy = (200 + 20y + (10x + xy)) Reorder the terms: 40x + xy = (200 + 10x + xy + 20y) 40x + xy = (200 + 10x + xy + 20y) Add '-1xy' to each side of the equation. 40x + xy + -1xy = 200 + 10x + xy + -1xy + 20y Combine like terms: xy + -1xy = 0 40x + 0 = 200 + 10x + xy + -1xy + 20y 40x = 200 + 10x + xy + -1xy + 20y Combine like terms: xy + -1xy = 0 40x = 200 + 10x + 0 + 20y 40x = 200 + 10x + 20y Solving 40x = 200 + 10x + 20y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10x' to each side of the equation. 40x + -10x = 200 + 10x + -10x + 20y Combine like terms: 40x + -10x = 30x 30x = 200 + 10x + -10x + 20y Combine like terms: 10x + -10x = 0 30x = 200 + 0 + 20y 30x = 200 + 20y Divide each side by '30'. x = 6.666666667 + 0.6666666667y Simplifying x = 6.666666667 + 0.6666666667y
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