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Simplifying (2 + -1k) * x + -3y + 12 = 0 Reorder the terms for easier multiplication: x(2 + -1k) + -3y + 12 = 0 (2 * x + -1k * x) + -3y + 12 = 0 Reorder the terms: (-1kx + 2x) + -3y + 12 = 0 (-1kx + 2x) + -3y + 12 = 0 Reorder the terms: 12 + -1kx + 2x + -3y = 0 Solving 12 + -1kx + 2x + -3y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -1kx + 2x + -12 + -3y = 0 + -12 Reorder the terms: 12 + -12 + -1kx + 2x + -3y = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1kx + 2x + -3y = 0 + -12 -1kx + 2x + -3y = 0 + -12 Combine like terms: 0 + -12 = -12 -1kx + 2x + -3y = -12 Add '-2x' to each side of the equation. -1kx + 2x + -2x + -3y = -12 + -2x Combine like terms: 2x + -2x = 0 -1kx + 0 + -3y = -12 + -2x -1kx + -3y = -12 + -2x Add '3y' to each side of the equation. -1kx + -3y + 3y = -12 + -2x + 3y Combine like terms: -3y + 3y = 0 -1kx + 0 = -12 + -2x + 3y -1kx = -12 + -2x + 3y Divide each side by '-1x'. k = 12x-1 + 2 + -3x-1y Simplifying k = 12x-1 + 2 + -3x-1y Reorder the terms: k = 2 + 12x-1 + -3x-1y
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