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Simplifying 9k + -1(4K + 7) = 3 + -5(2 + -1k) Reorder the terms: 9k + -1(7 + 4K) = 3 + -5(2 + -1k) 9k + (7 * -1 + 4K * -1) = 3 + -5(2 + -1k) 9k + (-7 + -4K) = 3 + -5(2 + -1k) Reorder the terms: -7 + -4K + 9k = 3 + -5(2 + -1k) -7 + -4K + 9k = 3 + (2 * -5 + -1k * -5) -7 + -4K + 9k = 3 + (-10 + 5k) Combine like terms: 3 + -10 = -7 -7 + -4K + 9k = -7 + 5k Add '7' to each side of the equation. -7 + -4K + 7 + 9k = -7 + 7 + 5k Reorder the terms: -7 + 7 + -4K + 9k = -7 + 7 + 5k Combine like terms: -7 + 7 = 0 0 + -4K + 9k = -7 + 7 + 5k -4K + 9k = -7 + 7 + 5k Combine like terms: -7 + 7 = 0 -4K + 9k = 0 + 5k -4K + 9k = 5k Solving -4K + 9k = 5k Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-9k' to each side of the equation. -4K + 9k + -9k = 5k + -9k Combine like terms: 9k + -9k = 0 -4K + 0 = 5k + -9k -4K = 5k + -9k Combine like terms: 5k + -9k = -4k -4K = -4k Divide each side by '-4'. K = k Simplifying K = k
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