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Simplifying -9 + 6(2k + -6) = 9 + 4(7 + -5k) Reorder the terms: -9 + 6(-6 + 2k) = 9 + 4(7 + -5k) -9 + (-6 * 6 + 2k * 6) = 9 + 4(7 + -5k) -9 + (-36 + 12k) = 9 + 4(7 + -5k) Combine like terms: -9 + -36 = -45 -45 + 12k = 9 + 4(7 + -5k) -45 + 12k = 9 + (7 * 4 + -5k * 4) -45 + 12k = 9 + (28 + -20k) Combine like terms: 9 + 28 = 37 -45 + 12k = 37 + -20k Solving -45 + 12k = 37 + -20k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '20k' to each side of the equation. -45 + 12k + 20k = 37 + -20k + 20k Combine like terms: 12k + 20k = 32k -45 + 32k = 37 + -20k + 20k Combine like terms: -20k + 20k = 0 -45 + 32k = 37 + 0 -45 + 32k = 37 Add '45' to each side of the equation. -45 + 45 + 32k = 37 + 45 Combine like terms: -45 + 45 = 0 0 + 32k = 37 + 45 32k = 37 + 45 Combine like terms: 37 + 45 = 82 32k = 82 Divide each side by '32'. k = 2.5625 Simplifying k = 2.5625
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