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Simplifying 3(4k + 14) = 10k + -2(k + -7) Reorder the terms: 3(14 + 4k) = 10k + -2(k + -7) (14 * 3 + 4k * 3) = 10k + -2(k + -7) (42 + 12k) = 10k + -2(k + -7) Reorder the terms: 42 + 12k = 10k + -2(-7 + k) 42 + 12k = 10k + (-7 * -2 + k * -2) 42 + 12k = 10k + (14 + -2k) Reorder the terms: 42 + 12k = 14 + 10k + -2k Combine like terms: 10k + -2k = 8k 42 + 12k = 14 + 8k Solving 42 + 12k = 14 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 42 + 12k + -8k = 14 + 8k + -8k Combine like terms: 12k + -8k = 4k 42 + 4k = 14 + 8k + -8k Combine like terms: 8k + -8k = 0 42 + 4k = 14 + 0 42 + 4k = 14 Add '-42' to each side of the equation. 42 + -42 + 4k = 14 + -42 Combine like terms: 42 + -42 = 0 0 + 4k = 14 + -42 4k = 14 + -42 Combine like terms: 14 + -42 = -28 4k = -28 Divide each side by '4'. k = -7 Simplifying k = -7
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