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Simplifying 4k + 5(-1k + -1) = -5(1 + -2k) Reorder the terms: 4k + 5(-1 + -1k) = -5(1 + -2k) 4k + (-1 * 5 + -1k * 5) = -5(1 + -2k) 4k + (-5 + -5k) = -5(1 + -2k) Reorder the terms: -5 + 4k + -5k = -5(1 + -2k) Combine like terms: 4k + -5k = -1k -5 + -1k = -5(1 + -2k) -5 + -1k = (1 * -5 + -2k * -5) -5 + -1k = (-5 + 10k) Add '5' to each side of the equation. -5 + 5 + -1k = -5 + 5 + 10k Combine like terms: -5 + 5 = 0 0 + -1k = -5 + 5 + 10k -1k = -5 + 5 + 10k Combine like terms: -5 + 5 = 0 -1k = 0 + 10k -1k = 10k Solving -1k = 10k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10k' to each side of the equation. -1k + -10k = 10k + -10k Combine like terms: -1k + -10k = -11k -11k = 10k + -10k Combine like terms: 10k + -10k = 0 -11k = 0 Divide each side by '-11'. k = 0 Simplifying k = 0
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