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Simplifying (x + 3)(y + 5) = (x + 2)(y + 8) Reorder the terms: (3 + x)(y + 5) = (x + 2)(y + 8) Reorder the terms: (3 + x)(5 + y) = (x + 2)(y + 8) Multiply (3 + x) * (5 + y) (3(5 + y) + x(5 + y)) = (x + 2)(y + 8) ((5 * 3 + y * 3) + x(5 + y)) = (x + 2)(y + 8) ((15 + 3y) + x(5 + y)) = (x + 2)(y + 8) (15 + 3y + (5 * x + y * x)) = (x + 2)(y + 8) (15 + 3y + (5x + xy)) = (x + 2)(y + 8) Reorder the terms: (15 + 5x + xy + 3y) = (x + 2)(y + 8) (15 + 5x + xy + 3y) = (x + 2)(y + 8) Reorder the terms: 15 + 5x + xy + 3y = (2 + x)(y + 8) Reorder the terms: 15 + 5x + xy + 3y = (2 + x)(8 + y) Multiply (2 + x) * (8 + y) 15 + 5x + xy + 3y = (2(8 + y) + x(8 + y)) 15 + 5x + xy + 3y = ((8 * 2 + y * 2) + x(8 + y)) 15 + 5x + xy + 3y = ((16 + 2y) + x(8 + y)) 15 + 5x + xy + 3y = (16 + 2y + (8 * x + y * x)) 15 + 5x + xy + 3y = (16 + 2y + (8x + xy)) Reorder the terms: 15 + 5x + xy + 3y = (16 + 8x + xy + 2y) 15 + 5x + xy + 3y = (16 + 8x + xy + 2y) Add '-1xy' to each side of the equation. 15 + 5x + xy + -1xy + 3y = 16 + 8x + xy + -1xy + 2y Combine like terms: xy + -1xy = 0 15 + 5x + 0 + 3y = 16 + 8x + xy + -1xy + 2y 15 + 5x + 3y = 16 + 8x + xy + -1xy + 2y Combine like terms: xy + -1xy = 0 15 + 5x + 3y = 16 + 8x + 0 + 2y 15 + 5x + 3y = 16 + 8x + 2y Solving 15 + 5x + 3y = 16 + 8x + 2y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. 15 + 5x + -8x + 3y = 16 + 8x + -8x + 2y Combine like terms: 5x + -8x = -3x 15 + -3x + 3y = 16 + 8x + -8x + 2y Combine like terms: 8x + -8x = 0 15 + -3x + 3y = 16 + 0 + 2y 15 + -3x + 3y = 16 + 2y Add '-15' to each side of the equation. 15 + -3x + -15 + 3y = 16 + -15 + 2y Reorder the terms: 15 + -15 + -3x + 3y = 16 + -15 + 2y Combine like terms: 15 + -15 = 0 0 + -3x + 3y = 16 + -15 + 2y -3x + 3y = 16 + -15 + 2y Combine like terms: 16 + -15 = 1 -3x + 3y = 1 + 2y Add '-3y' to each side of the equation. -3x + 3y + -3y = 1 + 2y + -3y Combine like terms: 3y + -3y = 0 -3x + 0 = 1 + 2y + -3y -3x = 1 + 2y + -3y Combine like terms: 2y + -3y = -1y -3x = 1 + -1y Divide each side by '-3'. x = -0.3333333333 + 0.3333333333y Simplifying x = -0.3333333333 + 0.3333333333y
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