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Simplifying 29k + -20 = 5(7k + 1) + -6 Reorder the terms: -20 + 29k = 5(7k + 1) + -6 Reorder the terms: -20 + 29k = 5(1 + 7k) + -6 -20 + 29k = (1 * 5 + 7k * 5) + -6 -20 + 29k = (5 + 35k) + -6 Reorder the terms: -20 + 29k = 5 + -6 + 35k Combine like terms: 5 + -6 = -1 -20 + 29k = -1 + 35k Solving -20 + 29k = -1 + 35k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-35k' to each side of the equation. -20 + 29k + -35k = -1 + 35k + -35k Combine like terms: 29k + -35k = -6k -20 + -6k = -1 + 35k + -35k Combine like terms: 35k + -35k = 0 -20 + -6k = -1 + 0 -20 + -6k = -1 Add '20' to each side of the equation. -20 + 20 + -6k = -1 + 20 Combine like terms: -20 + 20 = 0 0 + -6k = -1 + 20 -6k = -1 + 20 Combine like terms: -1 + 20 = 19 -6k = 19 Divide each side by '-6'. k = -3.166666667 Simplifying k = -3.166666667
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