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Simplifying -7(k + 1) + -8(4 + -8k) = 0 Reorder the terms: -7(1 + k) + -8(4 + -8k) = 0 (1 * -7 + k * -7) + -8(4 + -8k) = 0 (-7 + -7k) + -8(4 + -8k) = 0 -7 + -7k + (4 * -8 + -8k * -8) = 0 -7 + -7k + (-32 + 64k) = 0 Reorder the terms: -7 + -32 + -7k + 64k = 0 Combine like terms: -7 + -32 = -39 -39 + -7k + 64k = 0 Combine like terms: -7k + 64k = 57k -39 + 57k = 0 Solving -39 + 57k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + 57k = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 57k = 0 + 39 57k = 0 + 39 Combine like terms: 0 + 39 = 39 57k = 39 Divide each side by '57'. k = 0.6842105263 Simplifying k = 0.6842105263
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