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Simplifying -51 = 8(7 + 8k) + -5(1 + 6k) -51 = (7 * 8 + 8k * 8) + -5(1 + 6k) -51 = (56 + 64k) + -5(1 + 6k) -51 = 56 + 64k + (1 * -5 + 6k * -5) -51 = 56 + 64k + (-5 + -30k) Reorder the terms: -51 = 56 + -5 + 64k + -30k Combine like terms: 56 + -5 = 51 -51 = 51 + 64k + -30k Combine like terms: 64k + -30k = 34k -51 = 51 + 34k Solving -51 = 51 + 34k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-34k' to each side of the equation. -51 + -34k = 51 + 34k + -34k Combine like terms: 34k + -34k = 0 -51 + -34k = 51 + 0 -51 + -34k = 51 Add '51' to each side of the equation. -51 + 51 + -34k = 51 + 51 Combine like terms: -51 + 51 = 0 0 + -34k = 51 + 51 -34k = 51 + 51 Combine like terms: 51 + 51 = 102 -34k = 102 Divide each side by '-34'. k = -3 Simplifying k = -3
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