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Simplifying (2k + 1) + -1(k + 1) = 13 + -1(2k + 1) Reorder the terms: (1 + 2k) + -1(k + 1) = 13 + -1(2k + 1) Remove parenthesis around (1 + 2k) 1 + 2k + -1(k + 1) = 13 + -1(2k + 1) Reorder the terms: 1 + 2k + -1(1 + k) = 13 + -1(2k + 1) 1 + 2k + (1 * -1 + k * -1) = 13 + -1(2k + 1) 1 + 2k + (-1 + -1k) = 13 + -1(2k + 1) Reorder the terms: 1 + -1 + 2k + -1k = 13 + -1(2k + 1) Combine like terms: 1 + -1 = 0 0 + 2k + -1k = 13 + -1(2k + 1) 2k + -1k = 13 + -1(2k + 1) Combine like terms: 2k + -1k = 1k 1k = 13 + -1(2k + 1) Reorder the terms: 1k = 13 + -1(1 + 2k) 1k = 13 + (1 * -1 + 2k * -1) 1k = 13 + (-1 + -2k) Combine like terms: 13 + -1 = 12 1k = 12 + -2k Solving 1k = 12 + -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 = 12 + -2k + 2k Combine like terms: 1k + 2k = 3k 3k = 12 + -2k + 2k Combine like terms: -2k + 2k = 0 3k = 12 + 0 3k = 12 Divide each side by '3'. k = 4 Simplifying k = 4
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