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Simplifying 2(5 + -8k) + -13 = 9(1 + -1k) + -12 (5 * 2 + -8k * 2) + -13 = 9(1 + -1k) + -12 (10 + -16k) + -13 = 9(1 + -1k) + -12 Reorder the terms: 10 + -13 + -16k = 9(1 + -1k) + -12 Combine like terms: 10 + -13 = -3 -3 + -16k = 9(1 + -1k) + -12 -3 + -16k = (1 * 9 + -1k * 9) + -12 -3 + -16k = (9 + -9k) + -12 Reorder the terms: -3 + -16k = 9 + -12 + -9k Combine like terms: 9 + -12 = -3 -3 + -16k = -3 + -9k Add '3' to each side of the equation. -3 + 3 + -16k = -3 + 3 + -9k Combine like terms: -3 + 3 = 0 0 + -16k = -3 + 3 + -9k -16k = -3 + 3 + -9k Combine like terms: -3 + 3 = 0 -16k = 0 + -9k -16k = -9k Solving -16k = -9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9k' to each side of the equation. -16k + 9k = -9k + 9k Combine like terms: -16k + 9k = -7k -7k = -9k + 9k Combine like terms: -9k + 9k = 0 -7k = 0 Divide each side by '-7'. k = 0 Simplifying k = 0
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