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Simplifying 0.005(3 + -1k) + 0.05(k + -7) = 1 (3 * 0.005 + -1k * 0.005) + 0.05(k + -7) = 1 (0.015 + -0.005k) + 0.05(k + -7) = 1 Reorder the terms: 0.015 + -0.005k + 0.05(-7 + k) = 1 0.015 + -0.005k + (-7 * 0.05 + k * 0.05) = 1 0.015 + -0.005k + (-0.35 + 0.05k) = 1 Reorder the terms: 0.015 + -0.35 + -0.005k + 0.05k = 1 Combine like terms: 0.015 + -0.35 = -0.335 -0.335 + -0.005k + 0.05k = 1 Combine like terms: -0.005k + 0.05k = 0.045k -0.335 + 0.045k = 1 Solving -0.335 + 0.045k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.335' to each side of the equation. -0.335 + 0.335 + 0.045k = 1 + 0.335 Combine like terms: -0.335 + 0.335 = 0.000 0.000 + 0.045k = 1 + 0.335 0.045k = 1 + 0.335 Combine like terms: 1 + 0.335 = 1.335 0.045k = 1.335 Divide each side by '0.045'. k = 29.66666667 Simplifying k = 29.66666667
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