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Simplifying 0.003(5 + -1k) + 0.03(k + -9) = 1 (5 * 0.003 + -1k * 0.003) + 0.03(k + -9) = 1 (0.015 + -0.003k) + 0.03(k + -9) = 1 Reorder the terms: 0.015 + -0.003k + 0.03(-9 + k) = 1 0.015 + -0.003k + (-9 * 0.03 + k * 0.03) = 1 0.015 + -0.003k + (-0.27 + 0.03k) = 1 Reorder the terms: 0.015 + -0.27 + -0.003k + 0.03k = 1 Combine like terms: 0.015 + -0.27 = -0.255 -0.255 + -0.003k + 0.03k = 1 Combine like terms: -0.003k + 0.03k = 0.027k -0.255 + 0.027k = 1 Solving -0.255 + 0.027k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.255' to each side of the equation. -0.255 + 0.255 + 0.027k = 1 + 0.255 Combine like terms: -0.255 + 0.255 = 0.000 0.000 + 0.027k = 1 + 0.255 0.027k = 1 + 0.255 Combine like terms: 1 + 0.255 = 1.255 0.027k = 1.255 Divide each side by '0.027'. k = 46.48148148 Simplifying k = 46.48148148
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