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Simplifying 0.006(6 + -1k) + 0.03(k + -9) = 1 (6 * 0.006 + -1k * 0.006) + 0.03(k + -9) = 1 (0.036 + -0.006k) + 0.03(k + -9) = 1 Reorder the terms: 0.036 + -0.006k + 0.03(-9 + k) = 1 0.036 + -0.006k + (-9 * 0.03 + k * 0.03) = 1 0.036 + -0.006k + (-0.27 + 0.03k) = 1 Reorder the terms: 0.036 + -0.27 + -0.006k + 0.03k = 1 Combine like terms: 0.036 + -0.27 = -0.234 -0.234 + -0.006k + 0.03k = 1 Combine like terms: -0.006k + 0.03k = 0.024k -0.234 + 0.024k = 1 Solving -0.234 + 0.024k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.234' to each side of the equation. -0.234 + 0.234 + 0.024k = 1 + 0.234 Combine like terms: -0.234 + 0.234 = 0.000 0.000 + 0.024k = 1 + 0.234 0.024k = 1 + 0.234 Combine like terms: 1 + 0.234 = 1.234 0.024k = 1.234 Divide each side by '0.024'. k = 51.41666667 Simplifying k = 51.41666667
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