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Simplifying 0.5(10k + 10) + -1(k + -2) = 0 Reorder the terms: 0.5(10 + 10k) + -1(k + -2) = 0 (10 * 0.5 + 10k * 0.5) + -1(k + -2) = 0 (5 + 5k) + -1(k + -2) = 0 Reorder the terms: 5 + 5k + -1(-2 + k) = 0 5 + 5k + (-2 * -1 + k * -1) = 0 5 + 5k + (2 + -1k) = 0 Reorder the terms: 5 + 2 + 5k + -1k = 0 Combine like terms: 5 + 2 = 7 7 + 5k + -1k = 0 Combine like terms: 5k + -1k = 4k 7 + 4k = 0 Solving 7 + 4k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4k = 0 + -7 4k = 0 + -7 Combine like terms: 0 + -7 = -7 4k = -7 Divide each side by '4'. k = -1.75 Simplifying k = -1.75
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