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Simplifying 5(k + -5) + 5(2 + -1k) = 1 + -8k + 4k Reorder the terms: 5(-5 + k) + 5(2 + -1k) = 1 + -8k + 4k (-5 * 5 + k * 5) + 5(2 + -1k) = 1 + -8k + 4k (-25 + 5k) + 5(2 + -1k) = 1 + -8k + 4k -25 + 5k + (2 * 5 + -1k * 5) = 1 + -8k + 4k -25 + 5k + (10 + -5k) = 1 + -8k + 4k Reorder the terms: -25 + 10 + 5k + -5k = 1 + -8k + 4k Combine like terms: -25 + 10 = -15 -15 + 5k + -5k = 1 + -8k + 4k Combine like terms: 5k + -5k = 0 -15 + 0 = 1 + -8k + 4k -15 = 1 + -8k + 4k Combine like terms: -8k + 4k = -4k -15 = 1 + -4k Solving -15 = 1 + -4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4k' to each side of the equation. -15 + 4k = 1 + -4k + 4k Combine like terms: -4k + 4k = 0 -15 + 4k = 1 + 0 -15 + 4k = 1 Add '15' to each side of the equation. -15 + 15 + 4k = 1 + 15 Combine like terms: -15 + 15 = 0 0 + 4k = 1 + 15 4k = 1 + 15 Combine like terms: 1 + 15 = 16 4k = 16 Divide each side by '4'. k = 4 Simplifying k = 4
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