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Simplifying 0.006(1 + -1k) + 0.04(k + -1) = 1 (1 * 0.006 + -1k * 0.006) + 0.04(k + -1) = 1 (0.006 + -0.006k) + 0.04(k + -1) = 1 Reorder the terms: 0.006 + -0.006k + 0.04(-1 + k) = 1 0.006 + -0.006k + (-1 * 0.04 + k * 0.04) = 1 0.006 + -0.006k + (-0.04 + 0.04k) = 1 Reorder the terms: 0.006 + -0.04 + -0.006k + 0.04k = 1 Combine like terms: 0.006 + -0.04 = -0.034 -0.034 + -0.006k + 0.04k = 1 Combine like terms: -0.006k + 0.04k = 0.034k -0.034 + 0.034k = 1 Solving -0.034 + 0.034k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.034' to each side of the equation. -0.034 + 0.034 + 0.034k = 1 + 0.034 Combine like terms: -0.034 + 0.034 = 0.000 0.000 + 0.034k = 1 + 0.034 0.034k = 1 + 0.034 Combine like terms: 1 + 0.034 = 1.034 0.034k = 1.034 Divide each side by '0.034'. k = 30.41176471 Simplifying k = 30.41176471
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