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Simplifying 7(6 + -7k) + -8k = 6k + 7 (6 * 7 + -7k * 7) + -8k = 6k + 7 (42 + -49k) + -8k = 6k + 7 Combine like terms: -49k + -8k = -57k 42 + -57k = 6k + 7 Reorder the terms: 42 + -57k = 7 + 6k Solving 42 + -57k = 7 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. 42 + -57k + -6k = 7 + 6k + -6k Combine like terms: -57k + -6k = -63k 42 + -63k = 7 + 6k + -6k Combine like terms: 6k + -6k = 0 42 + -63k = 7 + 0 42 + -63k = 7 Add '-42' to each side of the equation. 42 + -42 + -63k = 7 + -42 Combine like terms: 42 + -42 = 0 0 + -63k = 7 + -42 -63k = 7 + -42 Combine like terms: 7 + -42 = -35 -63k = -35 Divide each side by '-63'. k = 0.5555555556 Simplifying k = 0.5555555556
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