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Simplifying 0.005(5 + -1k) + 0.08(k + -8) = 1 (5 * 0.005 + -1k * 0.005) + 0.08(k + -8) = 1 (0.025 + -0.005k) + 0.08(k + -8) = 1 Reorder the terms: 0.025 + -0.005k + 0.08(-8 + k) = 1 0.025 + -0.005k + (-8 * 0.08 + k * 0.08) = 1 0.025 + -0.005k + (-0.64 + 0.08k) = 1 Reorder the terms: 0.025 + -0.64 + -0.005k + 0.08k = 1 Combine like terms: 0.025 + -0.64 = -0.615 -0.615 + -0.005k + 0.08k = 1 Combine like terms: -0.005k + 0.08k = 0.075k -0.615 + 0.075k = 1 Solving -0.615 + 0.075k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.615' to each side of the equation. -0.615 + 0.615 + 0.075k = 1 + 0.615 Combine like terms: -0.615 + 0.615 = 0.000 0.000 + 0.075k = 1 + 0.615 0.075k = 1 + 0.615 Combine like terms: 1 + 0.615 = 1.615 0.075k = 1.615 Divide each side by '0.075'. k = 21.53333333 Simplifying k = 21.53333333
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