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Simplifying (2k + -1) + -1(k + 9) = (2k + 7) + -1(2k + -1) Reorder the terms: (-1 + 2k) + -1(k + 9) = (2k + 7) + -1(2k + -1) Remove parenthesis around (-1 + 2k) -1 + 2k + -1(k + 9) = (2k + 7) + -1(2k + -1) Reorder the terms: -1 + 2k + -1(9 + k) = (2k + 7) + -1(2k + -1) -1 + 2k + (9 * -1 + k * -1) = (2k + 7) + -1(2k + -1) -1 + 2k + (-9 + -1k) = (2k + 7) + -1(2k + -1) Reorder the terms: -1 + -9 + 2k + -1k = (2k + 7) + -1(2k + -1) Combine like terms: -1 + -9 = -10 -10 + 2k + -1k = (2k + 7) + -1(2k + -1) Combine like terms: 2k + -1k = 1k -10 + 1k = (2k + 7) + -1(2k + -1) Reorder the terms: -10 + 1k = (7 + 2k) + -1(2k + -1) Remove parenthesis around (7 + 2k) -10 + 1k = 7 + 2k + -1(2k + -1) Reorder the terms: -10 + 1k = 7 + 2k + -1(-1 + 2k) -10 + 1k = 7 + 2k + (-1 * -1 + 2k * -1) -10 + 1k = 7 + 2k + (1 + -2k) Reorder the terms: -10 + 1k = 7 + 1 + 2k + -2k Combine like terms: 7 + 1 = 8 -10 + 1k = 8 + 2k + -2k Combine like terms: 2k + -2k = 0 -10 + 1k = 8 + 0 -10 + 1k = 8 Solving -10 + 1k = 8 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 1k = 8 + 10 Combine like terms: -10 + 10 = 0 0 + 1k = 8 + 10 1k = 8 + 10 Combine like terms: 8 + 10 = 18 1k = 18 Divide each side by '1'. k = 18 Simplifying k = 18
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