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Simplifying 8k + -38 = 7(6 + 7k) + -1k Reorder the terms: -38 + 8k = 7(6 + 7k) + -1k -38 + 8k = (6 * 7 + 7k * 7) + -1k -38 + 8k = (42 + 49k) + -1k Combine like terms: 49k + -1k = 48k -38 + 8k = 42 + 48k Solving -38 + 8k = 42 + 48k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-48k' to each side of the equation. -38 + 8k + -48k = 42 + 48k + -48k Combine like terms: 8k + -48k = -40k -38 + -40k = 42 + 48k + -48k Combine like terms: 48k + -48k = 0 -38 + -40k = 42 + 0 -38 + -40k = 42 Add '38' to each side of the equation. -38 + 38 + -40k = 42 + 38 Combine like terms: -38 + 38 = 0 0 + -40k = 42 + 38 -40k = 42 + 38 Combine like terms: 42 + 38 = 80 -40k = 80 Divide each side by '-40'. k = -2 Simplifying k = -2
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