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Simplifying 67 = -3(1 + 7k) + 7(7 + 6k) 67 = (1 * -3 + 7k * -3) + 7(7 + 6k) 67 = (-3 + -21k) + 7(7 + 6k) 67 = -3 + -21k + (7 * 7 + 6k * 7) 67 = -3 + -21k + (49 + 42k) Reorder the terms: 67 = -3 + 49 + -21k + 42k Combine like terms: -3 + 49 = 46 67 = 46 + -21k + 42k Combine like terms: -21k + 42k = 21k 67 = 46 + 21k Solving 67 = 46 + 21k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-21k' to each side of the equation. 67 + -21k = 46 + 21k + -21k Combine like terms: 21k + -21k = 0 67 + -21k = 46 + 0 67 + -21k = 46 Add '-67' to each side of the equation. 67 + -67 + -21k = 46 + -67 Combine like terms: 67 + -67 = 0 0 + -21k = 46 + -67 -21k = 46 + -67 Combine like terms: 46 + -67 = -21 -21k = -21 Divide each side by '-21'. k = 1 Simplifying k = 1
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