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