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Simplifying 3k + -1(5k + 6) + -4(1 + -1k) = 2 + 9(k + 1) Reorder the terms: 3k + -1(6 + 5k) + -4(1 + -1k) = 2 + 9(k + 1) 3k + (6 * -1 + 5k * -1) + -4(1 + -1k) = 2 + 9(k + 1) 3k + (-6 + -5k) + -4(1 + -1k) = 2 + 9(k + 1) 3k + -6 + -5k + (1 * -4 + -1k * -4) = 2 + 9(k + 1) 3k + -6 + -5k + (-4 + 4k) = 2 + 9(k + 1) Reorder the terms: -6 + -4 + 3k + -5k + 4k = 2 + 9(k + 1) Combine like terms: -6 + -4 = -10 -10 + 3k + -5k + 4k = 2 + 9(k + 1) Combine like terms: 3k + -5k = -2k -10 + -2k + 4k = 2 + 9(k + 1) Combine like terms: -2k + 4k = 2k -10 + 2k = 2 + 9(k + 1) Reorder the terms: -10 + 2k = 2 + 9(1 + k) -10 + 2k = 2 + (1 * 9 + k * 9) -10 + 2k = 2 + (9 + 9k) Combine like terms: 2 + 9 = 11 -10 + 2k = 11 + 9k Solving -10 + 2k = 11 + 9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9k' to each side of the equation. -10 + 2k + -9k = 11 + 9k + -9k Combine like terms: 2k + -9k = -7k -10 + -7k = 11 + 9k + -9k Combine like terms: 9k + -9k = 0 -10 + -7k = 11 + 0 -10 + -7k = 11 Add '10' to each side of the equation. -10 + 10 + -7k = 11 + 10 Combine like terms: -10 + 10 = 0 0 + -7k = 11 + 10 -7k = 11 + 10 Combine like terms: 11 + 10 = 21 -7k = 21 Divide each side by '-7'. k = -3 Simplifying k = -3
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