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Simplifying 5(k + 4) + -2(k + 6) = 5(k + 1) + -1 Reorder the terms: 5(4 + k) + -2(k + 6) = 5(k + 1) + -1 (4 * 5 + k * 5) + -2(k + 6) = 5(k + 1) + -1 (20 + 5k) + -2(k + 6) = 5(k + 1) + -1 Reorder the terms: 20 + 5k + -2(6 + k) = 5(k + 1) + -1 20 + 5k + (6 * -2 + k * -2) = 5(k + 1) + -1 20 + 5k + (-12 + -2k) = 5(k + 1) + -1 Reorder the terms: 20 + -12 + 5k + -2k = 5(k + 1) + -1 Combine like terms: 20 + -12 = 8 8 + 5k + -2k = 5(k + 1) + -1 Combine like terms: 5k + -2k = 3k 8 + 3k = 5(k + 1) + -1 Reorder the terms: 8 + 3k = 5(1 + k) + -1 8 + 3k = (1 * 5 + k * 5) + -1 8 + 3k = (5 + 5k) + -1 Reorder the terms: 8 + 3k = 5 + -1 + 5k Combine like terms: 5 + -1 = 4 8 + 3k = 4 + 5k Solving 8 + 3k = 4 + 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. 8 + 3k + -5k = 4 + 5k + -5k Combine like terms: 3k + -5k = -2k 8 + -2k = 4 + 5k + -5k Combine like terms: 5k + -5k = 0 8 + -2k = 4 + 0 8 + -2k = 4 Add '-8' to each side of the equation. 8 + -8 + -2k = 4 + -8 Combine like terms: 8 + -8 = 0 0 + -2k = 4 + -8 -2k = 4 + -8 Combine like terms: 4 + -8 = -4 -2k = -4 Divide each side by '-2'. k = 2 Simplifying k = 2
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