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Simplifying k + 6 + 1 = 5(1k + -3) + -1(3k + -7) Reorder the terms: 6 + 1 + k = 5(1k + -3) + -1(3k + -7) Combine like terms: 6 + 1 = 7 7 + k = 5(1k + -3) + -1(3k + -7) Reorder the terms: 7 + k = 5(-3 + 1k) + -1(3k + -7) 7 + k = (-3 * 5 + 1k * 5) + -1(3k + -7) 7 + k = (-15 + 5k) + -1(3k + -7) Reorder the terms: 7 + k = -15 + 5k + -1(-7 + 3k) 7 + k = -15 + 5k + (-7 * -1 + 3k * -1) 7 + k = -15 + 5k + (7 + -3k) Reorder the terms: 7 + k = -15 + 7 + 5k + -3k Combine like terms: -15 + 7 = -8 7 + k = -8 + 5k + -3k Combine like terms: 5k + -3k = 2k 7 + k = -8 + 2k Solving 7 + k = -8 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 7 + k + -2k = -8 + 2k + -2k Combine like terms: k + -2k = -1k 7 + -1k = -8 + 2k + -2k Combine like terms: 2k + -2k = 0 7 + -1k = -8 + 0 7 + -1k = -8 Add '-7' to each side of the equation. 7 + -7 + -1k = -8 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = -8 + -7 -1k = -8 + -7 Combine like terms: -8 + -7 = -15 -1k = -15 Divide each side by '-1'. k = 15 Simplifying k = 15
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