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Simplifying 0.009(3 + -1k) + 0.01(k + -3) = 1 (3 * 0.009 + -1k * 0.009) + 0.01(k + -3) = 1 (0.027 + -0.009k) + 0.01(k + -3) = 1 Reorder the terms: 0.027 + -0.009k + 0.01(-3 + k) = 1 0.027 + -0.009k + (-3 * 0.01 + k * 0.01) = 1 0.027 + -0.009k + (-0.03 + 0.01k) = 1 Reorder the terms: 0.027 + -0.03 + -0.009k + 0.01k = 1 Combine like terms: 0.027 + -0.03 = -0.003 -0.003 + -0.009k + 0.01k = 1 Combine like terms: -0.009k + 0.01k = 0.001k -0.003 + 0.001k = 1 Solving -0.003 + 0.001k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.003' to each side of the equation. -0.003 + 0.003 + 0.001k = 1 + 0.003 Combine like terms: -0.003 + 0.003 = 0.000 0.000 + 0.001k = 1 + 0.003 0.001k = 1 + 0.003 Combine like terms: 1 + 0.003 = 1.003 0.001k = 1.003 Divide each side by '0.001'. k = 1003 Simplifying k = 1003
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