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Simplifying -89 = 3(2 + -5k) + 5(1 + 7k) -89 = (2 * 3 + -5k * 3) + 5(1 + 7k) -89 = (6 + -15k) + 5(1 + 7k) -89 = 6 + -15k + (1 * 5 + 7k * 5) -89 = 6 + -15k + (5 + 35k) Reorder the terms: -89 = 6 + 5 + -15k + 35k Combine like terms: 6 + 5 = 11 -89 = 11 + -15k + 35k Combine like terms: -15k + 35k = 20k -89 = 11 + 20k Solving -89 = 11 + 20k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-20k' to each side of the equation. -89 + -20k = 11 + 20k + -20k Combine like terms: 20k + -20k = 0 -89 + -20k = 11 + 0 -89 + -20k = 11 Add '89' to each side of the equation. -89 + 89 + -20k = 11 + 89 Combine like terms: -89 + 89 = 0 0 + -20k = 11 + 89 -20k = 11 + 89 Combine like terms: 11 + 89 = 100 -20k = 100 Divide each side by '-20'. k = -5 Simplifying k = -5
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