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Simplifying 3(4k + 14) = 10k + -1(k + -7) Reorder the terms: 3(14 + 4k) = 10k + -1(k + -7) (14 * 3 + 4k * 3) = 10k + -1(k + -7) (42 + 12k) = 10k + -1(k + -7) Reorder the terms: 42 + 12k = 10k + -1(-7 + k) 42 + 12k = 10k + (-7 * -1 + k * -1) 42 + 12k = 10k + (7 + -1k) Reorder the terms: 42 + 12k = 7 + 10k + -1k Combine like terms: 10k + -1k = 9k 42 + 12k = 7 + 9k Solving 42 + 12k = 7 + 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. 42 + 12k + -9k = 7 + 9k + -9k Combine like terms: 12k + -9k = 3k 42 + 3k = 7 + 9k + -9k Combine like terms: 9k + -9k = 0 42 + 3k = 7 + 0 42 + 3k = 7 Add '-42' to each side of the equation. 42 + -42 + 3k = 7 + -42 Combine like terms: 42 + -42 = 0 0 + 3k = 7 + -42 3k = 7 + -42 Combine like terms: 7 + -42 = -35 3k = -35 Divide each side by '3'. k = -11.66666667 Simplifying k = -11.66666667
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