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Simplifying 0.009(8 + -1k) + 0.04(k + -4) = 1 (8 * 0.009 + -1k * 0.009) + 0.04(k + -4) = 1 (0.072 + -0.009k) + 0.04(k + -4) = 1 Reorder the terms: 0.072 + -0.009k + 0.04(-4 + k) = 1 0.072 + -0.009k + (-4 * 0.04 + k * 0.04) = 1 0.072 + -0.009k + (-0.16 + 0.04k) = 1 Reorder the terms: 0.072 + -0.16 + -0.009k + 0.04k = 1 Combine like terms: 0.072 + -0.16 = -0.088 -0.088 + -0.009k + 0.04k = 1 Combine like terms: -0.009k + 0.04k = 0.031k -0.088 + 0.031k = 1 Solving -0.088 + 0.031k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.088' to each side of the equation. -0.088 + 0.088 + 0.031k = 1 + 0.088 Combine like terms: -0.088 + 0.088 = 0.000 0.000 + 0.031k = 1 + 0.088 0.031k = 1 + 0.088 Combine like terms: 1 + 0.088 = 1.088 0.031k = 1.088 Divide each side by '0.031'. k = 35.09677419 Simplifying k = 35.09677419
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