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Simplifying 7(3k + -2) + 5 = 6(2k + -1) + 24 Reorder the terms: 7(-2 + 3k) + 5 = 6(2k + -1) + 24 (-2 * 7 + 3k * 7) + 5 = 6(2k + -1) + 24 (-14 + 21k) + 5 = 6(2k + -1) + 24 Reorder the terms: -14 + 5 + 21k = 6(2k + -1) + 24 Combine like terms: -14 + 5 = -9 -9 + 21k = 6(2k + -1) + 24 Reorder the terms: -9 + 21k = 6(-1 + 2k) + 24 -9 + 21k = (-1 * 6 + 2k * 6) + 24 -9 + 21k = (-6 + 12k) + 24 Reorder the terms: -9 + 21k = -6 + 24 + 12k Combine like terms: -6 + 24 = 18 -9 + 21k = 18 + 12k Solving -9 + 21k = 18 + 12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12k' to each side of the equation. -9 + 21k + -12k = 18 + 12k + -12k Combine like terms: 21k + -12k = 9k -9 + 9k = 18 + 12k + -12k Combine like terms: 12k + -12k = 0 -9 + 9k = 18 + 0 -9 + 9k = 18 Add '9' to each side of the equation. -9 + 9 + 9k = 18 + 9 Combine like terms: -9 + 9 = 0 0 + 9k = 18 + 9 9k = 18 + 9 Combine like terms: 18 + 9 = 27 9k = 27 Divide each side by '9'. k = 3 Simplifying k = 3
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