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Simplifying 5(1 + k) + -1(7k + -7) = 0 (1 * 5 + k * 5) + -1(7k + -7) = 0 (5 + 5k) + -1(7k + -7) = 0 Reorder the terms: 5 + 5k + -1(-7 + 7k) = 0 5 + 5k + (-7 * -1 + 7k * -1) = 0 5 + 5k + (7 + -7k) = 0 Reorder the terms: 5 + 7 + 5k + -7k = 0 Combine like terms: 5 + 7 = 12 12 + 5k + -7k = 0 Combine like terms: 5k + -7k = -2k 12 + -2k = 0 Solving 12 + -2k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -2k = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -2k = 0 + -12 -2k = 0 + -12 Combine like terms: 0 + -12 = -12 -2k = -12 Divide each side by '-2'. k = 6 Simplifying k = 6
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