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Simplifying f(x) + f(2x + y) + 5xy = f(3x + -1y) + 2x + -2 + 1 Multiply f * x fx + f(2x + y) + 5xy = f(3x + -1y) + 2x + -2 + 1 fx + (2x * f + y * f) + 5xy = f(3x + -1y) + 2x + -2 + 1 fx + (2fx + fy) + 5xy = f(3x + -1y) + 2x + -2 + 1 Combine like terms: fx + 2fx = 3fx 3fx + fy + 5xy = f(3x + -1y) + 2x + -2 + 1 3fx + fy + 5xy = (3x * f + -1y * f) + 2x + -2 + 1 3fx + fy + 5xy = (3fx + -1fy) + 2x + -2 + 1 Reorder the terms: 3fx + fy + 5xy = -2 + 1 + 3fx + -1fy + 2x Combine like terms: -2 + 1 = -1 3fx + fy + 5xy = -1 + 3fx + -1fy + 2x Add '-3fx' to each side of the equation. 3fx + fy + -3fx + 5xy = -1 + 3fx + -1fy + -3fx + 2x Reorder the terms: 3fx + -3fx + fy + 5xy = -1 + 3fx + -1fy + -3fx + 2x Combine like terms: 3fx + -3fx = 0 0 + fy + 5xy = -1 + 3fx + -1fy + -3fx + 2x fy + 5xy = -1 + 3fx + -1fy + -3fx + 2x Reorder the terms: fy + 5xy = -1 + 3fx + -3fx + -1fy + 2x Combine like terms: 3fx + -3fx = 0 fy + 5xy = -1 + 0 + -1fy + 2x fy + 5xy = -1 + -1fy + 2x Solving fy + 5xy = -1 + -1fy + 2x Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add 'fy' to each side of the equation. fy + fy + 5xy = -1 + -1fy + fy + 2x Combine like terms: fy + fy = 2fy 2fy + 5xy = -1 + -1fy + fy + 2x Combine like terms: -1fy + fy = 0 2fy + 5xy = -1 + 0 + 2x 2fy + 5xy = -1 + 2x Add '-5xy' to each side of the equation. 2fy + 5xy + -5xy = -1 + 2x + -5xy Combine like terms: 5xy + -5xy = 0 2fy + 0 = -1 + 2x + -5xy 2fy = -1 + 2x + -5xy Divide each side by '2y'. f = -0.5y-1 + xy-1 + -2.5x Simplifying f = -0.5y-1 + xy-1 + -2.5x Reorder the terms: f = -2.5x + xy-1 + -0.5y-1
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