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Simplifying 0.04(k + 10) + 0.06(k + -30) = 7.6 Reorder the terms: 0.04(10 + k) + 0.06(k + -30) = 7.6 (10 * 0.04 + k * 0.04) + 0.06(k + -30) = 7.6 (0.4 + 0.04k) + 0.06(k + -30) = 7.6 Reorder the terms: 0.4 + 0.04k + 0.06(-30 + k) = 7.6 0.4 + 0.04k + (-30 * 0.06 + k * 0.06) = 7.6 0.4 + 0.04k + (-1.8 + 0.06k) = 7.6 Reorder the terms: 0.4 + -1.8 + 0.04k + 0.06k = 7.6 Combine like terms: 0.4 + -1.8 = -1.4 -1.4 + 0.04k + 0.06k = 7.6 Combine like terms: 0.04k + 0.06k = 0.1k -1.4 + 0.1k = 7.6 Solving -1.4 + 0.1k = 7.6 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + 0.1k = 7.6 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 0.1k = 7.6 + 1.4 0.1k = 7.6 + 1.4 Combine like terms: 7.6 + 1.4 = 9 0.1k = 9 Divide each side by '0.1'. k = 90 Simplifying k = 90
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