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Simplifying -7 = 0.75(3 + -10k) + (-5) -7 = (3 * 0.75 + -10k * 0.75) + (-5) -7 = (2.25 + -7.5k) + (-5) -7 = 2.25 + -7.5k + -5 Reorder the terms: -7 = 2.25 + -5 + -7.5k Combine like terms: 2.25 + -5 = -2.75 -7 = -2.75 + -7.5k Solving -7 = -2.75 + -7.5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7.5k' to each side of the equation. -7 + 7.5k = -2.75 + -7.5k + 7.5k Combine like terms: -7.5k + 7.5k = 0.0 -7 + 7.5k = -2.75 + 0.0 -7 + 7.5k = -2.75 Add '7' to each side of the equation. -7 + 7 + 7.5k = -2.75 + 7 Combine like terms: -7 + 7 = 0 0 + 7.5k = -2.75 + 7 7.5k = -2.75 + 7 Combine like terms: -2.75 + 7 = 4.25 7.5k = 4.25 Divide each side by '7.5'. k = 0.5666666667 Simplifying k = 0.5666666667
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