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Simplifying 47 = 5(1 + -3k) + 6(k + 4) 47 = (1 * 5 + -3k * 5) + 6(k + 4) 47 = (5 + -15k) + 6(k + 4) Reorder the terms: 47 = 5 + -15k + 6(4 + k) 47 = 5 + -15k + (4 * 6 + k * 6) 47 = 5 + -15k + (24 + 6k) Reorder the terms: 47 = 5 + 24 + -15k + 6k Combine like terms: 5 + 24 = 29 47 = 29 + -15k + 6k Combine like terms: -15k + 6k = -9k 47 = 29 + -9k Solving 47 = 29 + -9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9k' to each side of the equation. 47 + 9k = 29 + -9k + 9k Combine like terms: -9k + 9k = 0 47 + 9k = 29 + 0 47 + 9k = 29 Add '-47' to each side of the equation. 47 + -47 + 9k = 29 + -47 Combine like terms: 47 + -47 = 0 0 + 9k = 29 + -47 9k = 29 + -47 Combine like terms: 29 + -47 = -18 9k = -18 Divide each side by '9'. k = -2 Simplifying k = -2
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