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Simplifying -5(1 + 2k) + -8(-4 + 5k) = 0 (1 * -5 + 2k * -5) + -8(-4 + 5k) = 0 (-5 + -10k) + -8(-4 + 5k) = 0 -5 + -10k + (-4 * -8 + 5k * -8) = 0 -5 + -10k + (32 + -40k) = 0 Reorder the terms: -5 + 32 + -10k + -40k = 0 Combine like terms: -5 + 32 = 27 27 + -10k + -40k = 0 Combine like terms: -10k + -40k = -50k 27 + -50k = 0 Solving 27 + -50k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -50k = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -50k = 0 + -27 -50k = 0 + -27 Combine like terms: 0 + -27 = -27 -50k = -27 Divide each side by '-50'. k = 0.54 Simplifying k = 0.54
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