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Simplifying -34 = 8(1 + 6k) + 6(5 + -5k) -34 = (1 * 8 + 6k * 8) + 6(5 + -5k) -34 = (8 + 48k) + 6(5 + -5k) -34 = 8 + 48k + (5 * 6 + -5k * 6) -34 = 8 + 48k + (30 + -30k) Reorder the terms: -34 = 8 + 30 + 48k + -30k Combine like terms: 8 + 30 = 38 -34 = 38 + 48k + -30k Combine like terms: 48k + -30k = 18k -34 = 38 + 18k Solving -34 = 38 + 18k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18k' to each side of the equation. -34 + -18k = 38 + 18k + -18k Combine like terms: 18k + -18k = 0 -34 + -18k = 38 + 0 -34 + -18k = 38 Add '34' to each side of the equation. -34 + 34 + -18k = 38 + 34 Combine like terms: -34 + 34 = 0 0 + -18k = 38 + 34 -18k = 38 + 34 Combine like terms: 38 + 34 = 72 -18k = 72 Divide each side by '-18'. k = -4 Simplifying k = -4
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