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Simplifying 4000 = 40(1 + -2k) 4000 = (1 * 40 + -2k * 40) 4000 = (40 + -80k) Solving 4000 = 40 + -80k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '80k' to each side of the equation. 4000 + 80k = 40 + -80k + 80k Combine like terms: -80k + 80k = 0 4000 + 80k = 40 + 0 4000 + 80k = 40 Add '-4000' to each side of the equation. 4000 + -4000 + 80k = 40 + -4000 Combine like terms: 4000 + -4000 = 0 0 + 80k = 40 + -4000 80k = 40 + -4000 Combine like terms: 40 + -4000 = -3960 80k = -3960 Divide each side by '80'. k = -49.5 Simplifying k = -49.5
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