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Simplifying 6k + -3 + 2k + -6 = 7(2k + -1) + 8(1 + -1k) Reorder the terms: -3 + -6 + 6k + 2k = 7(2k + -1) + 8(1 + -1k) Combine like terms: -3 + -6 = -9 -9 + 6k + 2k = 7(2k + -1) + 8(1 + -1k) Combine like terms: 6k + 2k = 8k -9 + 8k = 7(2k + -1) + 8(1 + -1k) Reorder the terms: -9 + 8k = 7(-1 + 2k) + 8(1 + -1k) -9 + 8k = (-1 * 7 + 2k * 7) + 8(1 + -1k) -9 + 8k = (-7 + 14k) + 8(1 + -1k) -9 + 8k = -7 + 14k + (1 * 8 + -1k * 8) -9 + 8k = -7 + 14k + (8 + -8k) Reorder the terms: -9 + 8k = -7 + 8 + 14k + -8k Combine like terms: -7 + 8 = 1 -9 + 8k = 1 + 14k + -8k Combine like terms: 14k + -8k = 6k -9 + 8k = 1 + 6k Solving -9 + 8k = 1 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. -9 + 8k + -6k = 1 + 6k + -6k Combine like terms: 8k + -6k = 2k -9 + 2k = 1 + 6k + -6k Combine like terms: 6k + -6k = 0 -9 + 2k = 1 + 0 -9 + 2k = 1 Add '9' to each side of the equation. -9 + 9 + 2k = 1 + 9 Combine like terms: -9 + 9 = 0 0 + 2k = 1 + 9 2k = 1 + 9 Combine like terms: 1 + 9 = 10 2k = 10 Divide each side by '2'. k = 5 Simplifying k = 5
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