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Simplifying 12 + -1(3k + 10) + 4k = 3(2k + 1) + -11 Reorder the terms: 12 + -1(10 + 3k) + 4k = 3(2k + 1) + -11 12 + (10 * -1 + 3k * -1) + 4k = 3(2k + 1) + -11 12 + (-10 + -3k) + 4k = 3(2k + 1) + -11 Combine like terms: 12 + -10 = 2 2 + -3k + 4k = 3(2k + 1) + -11 Combine like terms: -3k + 4k = 1k 2 + 1k = 3(2k + 1) + -11 Reorder the terms: 2 + 1k = 3(1 + 2k) + -11 2 + 1k = (1 * 3 + 2k * 3) + -11 2 + 1k = (3 + 6k) + -11 Reorder the terms: 2 + 1k = 3 + -11 + 6k Combine like terms: 3 + -11 = -8 2 + 1k = -8 + 6k Solving 2 + 1k = -8 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. 2 + 1k + -6k = -8 + 6k + -6k Combine like terms: 1k + -6k = -5k 2 + -5k = -8 + 6k + -6k Combine like terms: 6k + -6k = 0 2 + -5k = -8 + 0 2 + -5k = -8 Add '-2' to each side of the equation. 2 + -2 + -5k = -8 + -2 Combine like terms: 2 + -2 = 0 0 + -5k = -8 + -2 -5k = -8 + -2 Combine like terms: -8 + -2 = -10 -5k = -10 Divide each side by '-5'. k = 2 Simplifying k = 2
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