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Simplifying 0.5(5 + -3k) = 6(k + 4) (5 * 0.5 + -3k * 0.5) = 6(k + 4) (2.5 + -1.5k) = 6(k + 4) Reorder the terms: 2.5 + -1.5k = 6(4 + k) 2.5 + -1.5k = (4 * 6 + k * 6) 2.5 + -1.5k = (24 + 6k) Solving 2.5 + -1.5k = 24 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. 2.5 + -1.5k + -6k = 24 + 6k + -6k Combine like terms: -1.5k + -6k = -7.5k 2.5 + -7.5k = 24 + 6k + -6k Combine like terms: 6k + -6k = 0 2.5 + -7.5k = 24 + 0 2.5 + -7.5k = 24 Add '-2.5' to each side of the equation. 2.5 + -2.5 + -7.5k = 24 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -7.5k = 24 + -2.5 -7.5k = 24 + -2.5 Combine like terms: 24 + -2.5 = 21.5 -7.5k = 21.5 Divide each side by '-7.5'. k = -2.866666667 Simplifying k = -2.866666667
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