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Simplifying 9(k + 5) = 10(3k + -2) + -8k Reorder the terms: 9(5 + k) = 10(3k + -2) + -8k (5 * 9 + k * 9) = 10(3k + -2) + -8k (45 + 9k) = 10(3k + -2) + -8k Reorder the terms: 45 + 9k = 10(-2 + 3k) + -8k 45 + 9k = (-2 * 10 + 3k * 10) + -8k 45 + 9k = (-20 + 30k) + -8k Combine like terms: 30k + -8k = 22k 45 + 9k = -20 + 22k Solving 45 + 9k = -20 + 22k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-22k' to each side of the equation. 45 + 9k + -22k = -20 + 22k + -22k Combine like terms: 9k + -22k = -13k 45 + -13k = -20 + 22k + -22k Combine like terms: 22k + -22k = 0 45 + -13k = -20 + 0 45 + -13k = -20 Add '-45' to each side of the equation. 45 + -45 + -13k = -20 + -45 Combine like terms: 45 + -45 = 0 0 + -13k = -20 + -45 -13k = -20 + -45 Combine like terms: -20 + -45 = -65 -13k = -65 Divide each side by '-13'. k = 5 Simplifying k = 5
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