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Simplifying 5k + -5k = 10(1 + -1k) + 6(k + 3) Combine like terms: 5k + -5k = 0 0 = 10(1 + -1k) + 6(k + 3) 0 = (1 * 10 + -1k * 10) + 6(k + 3) 0 = (10 + -10k) + 6(k + 3) Reorder the terms: 0 = 10 + -10k + 6(3 + k) 0 = 10 + -10k + (3 * 6 + k * 6) 0 = 10 + -10k + (18 + 6k) Reorder the terms: 0 = 10 + 18 + -10k + 6k Combine like terms: 10 + 18 = 28 0 = 28 + -10k + 6k Combine like terms: -10k + 6k = -4k 0 = 28 + -4k Solving 0 = 28 + -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. 0 + 4k = 28 + -4k + 4k Remove the zero: 4k = 28 + -4k + 4k Combine like terms: -4k + 4k = 0 4k = 28 + 0 4k = 28 Divide each side by '4'. k = 7 Simplifying k = 7
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