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Simplifying 9(3k + -5) = 12(3k + -1) + -51 Reorder the terms: 9(-5 + 3k) = 12(3k + -1) + -51 (-5 * 9 + 3k * 9) = 12(3k + -1) + -51 (-45 + 27k) = 12(3k + -1) + -51 Reorder the terms: -45 + 27k = 12(-1 + 3k) + -51 -45 + 27k = (-1 * 12 + 3k * 12) + -51 -45 + 27k = (-12 + 36k) + -51 Reorder the terms: -45 + 27k = -12 + -51 + 36k Combine like terms: -12 + -51 = -63 -45 + 27k = -63 + 36k Solving -45 + 27k = -63 + 36k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-36k' to each side of the equation. -45 + 27k + -36k = -63 + 36k + -36k Combine like terms: 27k + -36k = -9k -45 + -9k = -63 + 36k + -36k Combine like terms: 36k + -36k = 0 -45 + -9k = -63 + 0 -45 + -9k = -63 Add '45' to each side of the equation. -45 + 45 + -9k = -63 + 45 Combine like terms: -45 + 45 = 0 0 + -9k = -63 + 45 -9k = -63 + 45 Combine like terms: -63 + 45 = -18 -9k = -18 Divide each side by '-9'. k = 2 Simplifying k = 2
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