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Simplifying (x + 17)(y + 2) = (x + 22)(y + 1) Reorder the terms: (17 + x)(y + 2) = (x + 22)(y + 1) Reorder the terms: (17 + x)(2 + y) = (x + 22)(y + 1) Multiply (17 + x) * (2 + y) (17(2 + y) + x(2 + y)) = (x + 22)(y + 1) ((2 * 17 + y * 17) + x(2 + y)) = (x + 22)(y + 1) ((34 + 17y) + x(2 + y)) = (x + 22)(y + 1) (34 + 17y + (2 * x + y * x)) = (x + 22)(y + 1) (34 + 17y + (2x + xy)) = (x + 22)(y + 1) Reorder the terms: (34 + 2x + xy + 17y) = (x + 22)(y + 1) (34 + 2x + xy + 17y) = (x + 22)(y + 1) Reorder the terms: 34 + 2x + xy + 17y = (22 + x)(y + 1) Reorder the terms: 34 + 2x + xy + 17y = (22 + x)(1 + y) Multiply (22 + x) * (1 + y) 34 + 2x + xy + 17y = (22(1 + y) + x(1 + y)) 34 + 2x + xy + 17y = ((1 * 22 + y * 22) + x(1 + y)) 34 + 2x + xy + 17y = ((22 + 22y) + x(1 + y)) 34 + 2x + xy + 17y = (22 + 22y + (1 * x + y * x)) 34 + 2x + xy + 17y = (22 + 22y + (1x + xy)) Reorder the terms: 34 + 2x + xy + 17y = (22 + 1x + xy + 22y) 34 + 2x + xy + 17y = (22 + 1x + xy + 22y) Add '-1xy' to each side of the equation. 34 + 2x + xy + -1xy + 17y = 22 + 1x + xy + -1xy + 22y Combine like terms: xy + -1xy = 0 34 + 2x + 0 + 17y = 22 + 1x + xy + -1xy + 22y 34 + 2x + 17y = 22 + 1x + xy + -1xy + 22y Combine like terms: xy + -1xy = 0 34 + 2x + 17y = 22 + 1x + 0 + 22y 34 + 2x + 17y = 22 + 1x + 22y Solving 34 + 2x + 17y = 22 + 1x + 22y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 34 + 2x + -1x + 17y = 22 + 1x + -1x + 22y Combine like terms: 2x + -1x = 1x 34 + 1x + 17y = 22 + 1x + -1x + 22y Combine like terms: 1x + -1x = 0 34 + 1x + 17y = 22 + 0 + 22y 34 + 1x + 17y = 22 + 22y Add '-34' to each side of the equation. 34 + 1x + -34 + 17y = 22 + -34 + 22y Reorder the terms: 34 + -34 + 1x + 17y = 22 + -34 + 22y Combine like terms: 34 + -34 = 0 0 + 1x + 17y = 22 + -34 + 22y 1x + 17y = 22 + -34 + 22y Combine like terms: 22 + -34 = -12 1x + 17y = -12 + 22y Add '-17y' to each side of the equation. 1x + 17y + -17y = -12 + 22y + -17y Combine like terms: 17y + -17y = 0 1x + 0 = -12 + 22y + -17y 1x = -12 + 22y + -17y Combine like terms: 22y + -17y = 5y 1x = -12 + 5y Divide each side by '1'. x = -12 + 5y Simplifying x = -12 + 5y
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