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Simplifying -38 + -5k = -7k + 8(6k + 1) Reorder the terms: -38 + -5k = -7k + 8(1 + 6k) -38 + -5k = -7k + (1 * 8 + 6k * 8) -38 + -5k = -7k + (8 + 48k) Reorder the terms: -38 + -5k = 8 + -7k + 48k Combine like terms: -7k + 48k = 41k -38 + -5k = 8 + 41k Solving -38 + -5k = 8 + 41k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-41k' to each side of the equation. -38 + -5k + -41k = 8 + 41k + -41k Combine like terms: -5k + -41k = -46k -38 + -46k = 8 + 41k + -41k Combine like terms: 41k + -41k = 0 -38 + -46k = 8 + 0 -38 + -46k = 8 Add '38' to each side of the equation. -38 + 38 + -46k = 8 + 38 Combine like terms: -38 + 38 = 0 0 + -46k = 8 + 38 -46k = 8 + 38 Combine like terms: 8 + 38 = 46 -46k = 46 Divide each side by '-46'. k = -1 Simplifying k = -1
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