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Simplifying 3x + -2(x + -1k) + 4(-1k + -2x) + 1 = 0 Reorder the terms: 3x + -2(-1k + x) + 4(-1k + -2x) + 1 = 0 3x + (-1k * -2 + x * -2) + 4(-1k + -2x) + 1 = 0 3x + (2k + -2x) + 4(-1k + -2x) + 1 = 0 3x + 2k + -2x + (-1k * 4 + -2x * 4) + 1 = 0 3x + 2k + -2x + (-4k + -8x) + 1 = 0 Reorder the terms: 1 + 2k + -4k + 3x + -2x + -8x = 0 Combine like terms: 2k + -4k = -2k 1 + -2k + 3x + -2x + -8x = 0 Combine like terms: 3x + -2x = 1x 1 + -2k + 1x + -8x = 0 Combine like terms: 1x + -8x = -7x 1 + -2k + -7x = 0 Solving 1 + -2k + -7x = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -2k + -1 + -7x = 0 + -1 Reorder the terms: 1 + -1 + -2k + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2k + -7x = 0 + -1 -2k + -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -2k + -7x = -1 Add '7x' to each side of the equation. -2k + -7x + 7x = -1 + 7x Combine like terms: -7x + 7x = 0 -2k + 0 = -1 + 7x -2k = -1 + 7x Divide each side by '-2'. k = 0.5 + -3.5x Simplifying k = 0.5 + -3.5x
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