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Simplifying 0.006(7 + -1x) + 0.08(k + -7) = 1 (7 * 0.006 + -1x * 0.006) + 0.08(k + -7) = 1 (0.042 + -0.006x) + 0.08(k + -7) = 1 Reorder the terms: 0.042 + -0.006x + 0.08(-7 + k) = 1 0.042 + -0.006x + (-7 * 0.08 + k * 0.08) = 1 0.042 + -0.006x + (-0.56 + 0.08k) = 1 Reorder the terms: 0.042 + -0.56 + 0.08k + -0.006x = 1 Combine like terms: 0.042 + -0.56 = -0.518 -0.518 + 0.08k + -0.006x = 1 Solving -0.518 + 0.08k + -0.006x = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.518' to each side of the equation. -0.518 + 0.08k + 0.518 + -0.006x = 1 + 0.518 Reorder the terms: -0.518 + 0.518 + 0.08k + -0.006x = 1 + 0.518 Combine like terms: -0.518 + 0.518 = 0.000 0.000 + 0.08k + -0.006x = 1 + 0.518 0.08k + -0.006x = 1 + 0.518 Combine like terms: 1 + 0.518 = 1.518 0.08k + -0.006x = 1.518 Add '0.006x' to each side of the equation. 0.08k + -0.006x + 0.006x = 1.518 + 0.006x Combine like terms: -0.006x + 0.006x = 0.000 0.08k + 0.000 = 1.518 + 0.006x 0.08k = 1.518 + 0.006x Divide each side by '0.08'. k = 18.975 + 0.075x Simplifying k = 18.975 + 0.075x
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