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Simplifying -5(-4 + 4k) + -7(1 + -3k) = -4k + 7k (-4 * -5 + 4k * -5) + -7(1 + -3k) = -4k + 7k (20 + -20k) + -7(1 + -3k) = -4k + 7k 20 + -20k + (1 * -7 + -3k * -7) = -4k + 7k 20 + -20k + (-7 + 21k) = -4k + 7k Reorder the terms: 20 + -7 + -20k + 21k = -4k + 7k Combine like terms: 20 + -7 = 13 13 + -20k + 21k = -4k + 7k Combine like terms: -20k + 21k = 1k 13 + 1k = -4k + 7k Combine like terms: -4k + 7k = 3k 13 + 1k = 3k Solving 13 + 1k = 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. 13 + 1k + -3k = 3k + -3k Combine like terms: 1k + -3k = -2k 13 + -2k = 3k + -3k Combine like terms: 3k + -3k = 0 13 + -2k = 0 Add '-13' to each side of the equation. 13 + -13 + -2k = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2k = 0 + -13 -2k = 0 + -13 Combine like terms: 0 + -13 = -13 -2k = -13 Divide each side by '-2'. k = 6.5 Simplifying k = 6.5
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