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Simplifying [(5K + -3) + 1] + [(K + 2) + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Reorder the terms: [(-3 + 5K) + 1] + [(K + 2) + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Remove parenthesis around (-3 + 5K) [-3 + 5K + 1] + [(K + 2) + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Reorder the terms: [-3 + 1 + 5K] + [(K + 2) + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Combine like terms: -3 + 1 = -2 [-2 + 5K] + [(K + 2) + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Remove brackets around [-2 + 5K] -2 + 5K + [(K + 2) + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Reorder the terms: -2 + 5K + [(2 + K) + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Remove parenthesis around (2 + K) -2 + 5K + [2 + K + 2] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Reorder the terms: -2 + 5K + [2 + 2 + K] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Combine like terms: 2 + 2 = 4 -2 + 5K + [4 + K] + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Remove brackets around [4 + K] -2 + 5K + 4 + K + [(3K + -11) + 3] = (K + 1) + (K + 2) + (K + 3) Reorder the terms: -2 + 5K + 4 + K + [(-11 + 3K) + 3] = (K + 1) + (K + 2) + (K + 3) Remove parenthesis around (-11 + 3K) -2 + 5K + 4 + K + [-11 + 3K + 3] = (K + 1) + (K + 2) + (K + 3) Reorder the terms: -2 + 5K + 4 + K + [-11 + 3 + 3K] = (K + 1) + (K + 2) + (K + 3) Combine like terms: -11 + 3 = -8 -2 + 5K + 4 + K + [-8 + 3K] = (K + 1) + (K + 2) + (K + 3) Remove brackets around [-8 + 3K] -2 + 5K + 4 + K + -8 + 3K = (K + 1) + (K + 2) + (K + 3) Reorder the terms: -2 + 4 + -8 + 5K + K + 3K = (K + 1) + (K + 2) + (K + 3) Combine like terms: -2 + 4 = 2 2 + -8 + 5K + K + 3K = (K + 1) + (K + 2) + (K + 3) Combine like terms: 2 + -8 = -6 -6 + 5K + K + 3K = (K + 1) + (K + 2) + (K + 3) Combine like terms: 5K + K = 6K -6 + 6K + 3K = (K + 1) + (K + 2) + (K + 3) Combine like terms: 6K + 3K = 9K -6 + 9K = (K + 1) + (K + 2) + (K + 3) Reorder the terms: -6 + 9K = (1 + K) + (K + 2) + (K + 3) Remove parenthesis around (1 + K) -6 + 9K = 1 + K + (K + 2) + (K + 3) Reorder the terms: -6 + 9K = 1 + K + (2 + K) + (K + 3) Remove parenthesis around (2 + K) -6 + 9K = 1 + K + 2 + K + (K + 3) Reorder the terms: -6 + 9K = 1 + K + 2 + K + (3 + K) Remove parenthesis around (3 + K) -6 + 9K = 1 + K + 2 + K + 3 + K Reorder the terms: -6 + 9K = 1 + 2 + 3 + K + K + K Combine like terms: 1 + 2 = 3 -6 + 9K = 3 + 3 + K + K + K Combine like terms: 3 + 3 = 6 -6 + 9K = 6 + K + K + K Combine like terms: K + K = 2K -6 + 9K = 6 + 2K + K Combine like terms: 2K + K = 3K -6 + 9K = 6 + 3K Solving -6 + 9K = 6 + 3K Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-3K' to each side of the equation. -6 + 9K + -3K = 6 + 3K + -3K Combine like terms: 9K + -3K = 6K -6 + 6K = 6 + 3K + -3K Combine like terms: 3K + -3K = 0 -6 + 6K = 6 + 0 -6 + 6K = 6 Add '6' to each side of the equation. -6 + 6 + 6K = 6 + 6 Combine like terms: -6 + 6 = 0 0 + 6K = 6 + 6 6K = 6 + 6 Combine like terms: 6 + 6 = 12 6K = 12 Divide each side by '6'. K = 2 Simplifying K = 2
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