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Simplifying 0.005(8 + -1k) + 0.03(k + -9) = 1 (8 * 0.005 + -1k * 0.005) + 0.03(k + -9) = 1 (0.04 + -0.005k) + 0.03(k + -9) = 1 Reorder the terms: 0.04 + -0.005k + 0.03(-9 + k) = 1 0.04 + -0.005k + (-9 * 0.03 + k * 0.03) = 1 0.04 + -0.005k + (-0.27 + 0.03k) = 1 Reorder the terms: 0.04 + -0.27 + -0.005k + 0.03k = 1 Combine like terms: 0.04 + -0.27 = -0.23 -0.23 + -0.005k + 0.03k = 1 Combine like terms: -0.005k + 0.03k = 0.025k -0.23 + 0.025k = 1 Solving -0.23 + 0.025k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.23' to each side of the equation. -0.23 + 0.23 + 0.025k = 1 + 0.23 Combine like terms: -0.23 + 0.23 = 0.00 0.00 + 0.025k = 1 + 0.23 0.025k = 1 + 0.23 Combine like terms: 1 + 0.23 = 1.23 0.025k = 1.23 Divide each side by '0.025'. k = 49.2 Simplifying k = 49.2
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