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Simplifying (x + 5)(y + -2) = (x + 2)(y + -1) Reorder the terms: (5 + x)(y + -2) = (x + 2)(y + -1) Reorder the terms: (5 + x)(-2 + y) = (x + 2)(y + -1) Multiply (5 + x) * (-2 + y) (5(-2 + y) + x(-2 + y)) = (x + 2)(y + -1) ((-2 * 5 + y * 5) + x(-2 + y)) = (x + 2)(y + -1) ((-10 + 5y) + x(-2 + y)) = (x + 2)(y + -1) (-10 + 5y + (-2 * x + y * x)) = (x + 2)(y + -1) (-10 + 5y + (-2x + xy)) = (x + 2)(y + -1) Reorder the terms: (-10 + -2x + xy + 5y) = (x + 2)(y + -1) (-10 + -2x + xy + 5y) = (x + 2)(y + -1) Reorder the terms: -10 + -2x + xy + 5y = (2 + x)(y + -1) Reorder the terms: -10 + -2x + xy + 5y = (2 + x)(-1 + y) Multiply (2 + x) * (-1 + y) -10 + -2x + xy + 5y = (2(-1 + y) + x(-1 + y)) -10 + -2x + xy + 5y = ((-1 * 2 + y * 2) + x(-1 + y)) -10 + -2x + xy + 5y = ((-2 + 2y) + x(-1 + y)) -10 + -2x + xy + 5y = (-2 + 2y + (-1 * x + y * x)) -10 + -2x + xy + 5y = (-2 + 2y + (-1x + xy)) Reorder the terms: -10 + -2x + xy + 5y = (-2 + -1x + xy + 2y) -10 + -2x + xy + 5y = (-2 + -1x + xy + 2y) Add '-1xy' to each side of the equation. -10 + -2x + xy + -1xy + 5y = -2 + -1x + xy + -1xy + 2y Combine like terms: xy + -1xy = 0 -10 + -2x + 0 + 5y = -2 + -1x + xy + -1xy + 2y -10 + -2x + 5y = -2 + -1x + xy + -1xy + 2y Combine like terms: xy + -1xy = 0 -10 + -2x + 5y = -2 + -1x + 0 + 2y -10 + -2x + 5y = -2 + -1x + 2y Solving -10 + -2x + 5y = -2 + -1x + 2y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'x' to each side of the equation. -10 + -2x + x + 5y = -2 + -1x + x + 2y Combine like terms: -2x + x = -1x -10 + -1x + 5y = -2 + -1x + x + 2y Combine like terms: -1x + x = 0 -10 + -1x + 5y = -2 + 0 + 2y -10 + -1x + 5y = -2 + 2y Add '10' to each side of the equation. -10 + -1x + 10 + 5y = -2 + 10 + 2y Reorder the terms: -10 + 10 + -1x + 5y = -2 + 10 + 2y Combine like terms: -10 + 10 = 0 0 + -1x + 5y = -2 + 10 + 2y -1x + 5y = -2 + 10 + 2y Combine like terms: -2 + 10 = 8 -1x + 5y = 8 + 2y Add '-5y' to each side of the equation. -1x + 5y + -5y = 8 + 2y + -5y Combine like terms: 5y + -5y = 0 -1x + 0 = 8 + 2y + -5y -1x = 8 + 2y + -5y Combine like terms: 2y + -5y = -3y -1x = 8 + -3y Divide each side by '-1'. x = -8 + 3y Simplifying x = -8 + 3y
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