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Simplifying -7(1 + -2k) = 7k + 3(k + -1) (1 * -7 + -2k * -7) = 7k + 3(k + -1) (-7 + 14k) = 7k + 3(k + -1) Reorder the terms: -7 + 14k = 7k + 3(-1 + k) -7 + 14k = 7k + (-1 * 3 + k * 3) -7 + 14k = 7k + (-3 + 3k) Reorder the terms: -7 + 14k = -3 + 7k + 3k Combine like terms: 7k + 3k = 10k -7 + 14k = -3 + 10k Solving -7 + 14k = -3 + 10k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10k' to each side of the equation. -7 + 14k + -10k = -3 + 10k + -10k Combine like terms: 14k + -10k = 4k -7 + 4k = -3 + 10k + -10k Combine like terms: 10k + -10k = 0 -7 + 4k = -3 + 0 -7 + 4k = -3 Add '7' to each side of the equation. -7 + 7 + 4k = -3 + 7 Combine like terms: -7 + 7 = 0 0 + 4k = -3 + 7 4k = -3 + 7 Combine like terms: -3 + 7 = 4 4k = 4 Divide each side by '4'. k = 1 Simplifying k = 1
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