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Simplifying 8 + -1(4k + 7) = 5(k + 6) + -2 Reorder the terms: 8 + -1(7 + 4k) = 5(k + 6) + -2 8 + (7 * -1 + 4k * -1) = 5(k + 6) + -2 8 + (-7 + -4k) = 5(k + 6) + -2 Combine like terms: 8 + -7 = 1 1 + -4k = 5(k + 6) + -2 Reorder the terms: 1 + -4k = 5(6 + k) + -2 1 + -4k = (6 * 5 + k * 5) + -2 1 + -4k = (30 + 5k) + -2 Reorder the terms: 1 + -4k = 30 + -2 + 5k Combine like terms: 30 + -2 = 28 1 + -4k = 28 + 5k Solving 1 + -4k = 28 + 5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5k' to each side of the equation. 1 + -4k + -5k = 28 + 5k + -5k Combine like terms: -4k + -5k = -9k 1 + -9k = 28 + 5k + -5k Combine like terms: 5k + -5k = 0 1 + -9k = 28 + 0 1 + -9k = 28 Add '-1' to each side of the equation. 1 + -1 + -9k = 28 + -1 Combine like terms: 1 + -1 = 0 0 + -9k = 28 + -1 -9k = 28 + -1 Combine like terms: 28 + -1 = 27 -9k = 27 Divide each side by '-9'. k = -3 Simplifying k = -3
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