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Simplifying 5(k + 6) + 3(k + -4) = 42 Reorder the terms: 5(6 + k) + 3(k + -4) = 42 (6 * 5 + k * 5) + 3(k + -4) = 42 (30 + 5k) + 3(k + -4) = 42 Reorder the terms: 30 + 5k + 3(-4 + k) = 42 30 + 5k + (-4 * 3 + k * 3) = 42 30 + 5k + (-12 + 3k) = 42 Reorder the terms: 30 + -12 + 5k + 3k = 42 Combine like terms: 30 + -12 = 18 18 + 5k + 3k = 42 Combine like terms: 5k + 3k = 8k 18 + 8k = 42 Solving 18 + 8k = 42 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + 8k = 42 + -18 Combine like terms: 18 + -18 = 0 0 + 8k = 42 + -18 8k = 42 + -18 Combine like terms: 42 + -18 = 24 8k = 24 Divide each side by '8'. k = 3 Simplifying k = 3
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