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Simplifying -5(1 + -5k) + 5(-8k + -2) = -4k + -8k (1 * -5 + -5k * -5) + 5(-8k + -2) = -4k + -8k (-5 + 25k) + 5(-8k + -2) = -4k + -8k Reorder the terms: -5 + 25k + 5(-2 + -8k) = -4k + -8k -5 + 25k + (-2 * 5 + -8k * 5) = -4k + -8k -5 + 25k + (-10 + -40k) = -4k + -8k Reorder the terms: -5 + -10 + 25k + -40k = -4k + -8k Combine like terms: -5 + -10 = -15 -15 + 25k + -40k = -4k + -8k Combine like terms: 25k + -40k = -15k -15 + -15k = -4k + -8k Combine like terms: -4k + -8k = -12k -15 + -15k = -12k Solving -15 + -15k = -12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12k' to each side of the equation. -15 + -15k + 12k = -12k + 12k Combine like terms: -15k + 12k = -3k -15 + -3k = -12k + 12k Combine like terms: -12k + 12k = 0 -15 + -3k = 0 Add '15' to each side of the equation. -15 + 15 + -3k = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -3k = 0 + 15 -3k = 0 + 15 Combine like terms: 0 + 15 = 15 -3k = 15 Divide each side by '-3'. k = -5 Simplifying k = -5
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