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Simplifying -7(k + 1) + 2(4k + 2) = -8k + -3 + 6k Reorder the terms: -7(1 + k) + 2(4k + 2) = -8k + -3 + 6k (1 * -7 + k * -7) + 2(4k + 2) = -8k + -3 + 6k (-7 + -7k) + 2(4k + 2) = -8k + -3 + 6k Reorder the terms: -7 + -7k + 2(2 + 4k) = -8k + -3 + 6k -7 + -7k + (2 * 2 + 4k * 2) = -8k + -3 + 6k -7 + -7k + (4 + 8k) = -8k + -3 + 6k Reorder the terms: -7 + 4 + -7k + 8k = -8k + -3 + 6k Combine like terms: -7 + 4 = -3 -3 + -7k + 8k = -8k + -3 + 6k Combine like terms: -7k + 8k = 1k -3 + 1k = -8k + -3 + 6k Reorder the terms: -3 + 1k = -3 + -8k + 6k Combine like terms: -8k + 6k = -2k -3 + 1k = -3 + -2k Add '3' to each side of the equation. -3 + 3 + 1k = -3 + 3 + -2k Combine like terms: -3 + 3 = 0 0 + 1k = -3 + 3 + -2k 1k = -3 + 3 + -2k Combine like terms: -3 + 3 = 0 1k = 0 + -2k 1k = -2k Solving 1k = -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. 1k + 2k = -2k + 2k Combine like terms: 1k + 2k = 3k 3k = -2k + 2k Combine like terms: -2k + 2k = 0 3k = 0 Divide each side by '3'. k = 0 Simplifying k = 0
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