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Simplifying 0.5(1.2k + 6) = 7.1k + 34.4 Reorder the terms: 0.5(6 + 1.2k) = 7.1k + 34.4 (6 * 0.5 + 1.2k * 0.5) = 7.1k + 34.4 (3 + 0.6k) = 7.1k + 34.4 Reorder the terms: 3 + 0.6k = 34.4 + 7.1k Solving 3 + 0.6k = 34.4 + 7.1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7.1k' to each side of the equation. 3 + 0.6k + -7.1k = 34.4 + 7.1k + -7.1k Combine like terms: 0.6k + -7.1k = -6.5k 3 + -6.5k = 34.4 + 7.1k + -7.1k Combine like terms: 7.1k + -7.1k = 0.0 3 + -6.5k = 34.4 + 0.0 3 + -6.5k = 34.4 Add '-3' to each side of the equation. 3 + -3 + -6.5k = 34.4 + -3 Combine like terms: 3 + -3 = 0 0 + -6.5k = 34.4 + -3 -6.5k = 34.4 + -3 Combine like terms: 34.4 + -3 = 31.4 -6.5k = 31.4 Divide each side by '-6.5'. k = -4.830769231 Simplifying k = -4.830769231
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