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Simplifying 2 + -1(6k + 1) = 7[(4k + -1) + -1(k + -5)] Reorder the terms: 2 + -1(1 + 6k) = 7[(4k + -1) + -1(k + -5)] 2 + (1 * -1 + 6k * -1) = 7[(4k + -1) + -1(k + -5)] 2 + (-1 + -6k) = 7[(4k + -1) + -1(k + -5)] Combine like terms: 2 + -1 = 1 1 + -6k = 7[(4k + -1) + -1(k + -5)] Reorder the terms: 1 + -6k = 7[(-1 + 4k) + -1(k + -5)] Remove parenthesis around (-1 + 4k) 1 + -6k = 7[-1 + 4k + -1(k + -5)] Reorder the terms: 1 + -6k = 7[-1 + 4k + -1(-5 + k)] 1 + -6k = 7[-1 + 4k + (-5 * -1 + k * -1)] 1 + -6k = 7[-1 + 4k + (5 + -1k)] Reorder the terms: 1 + -6k = 7[-1 + 5 + 4k + -1k] Combine like terms: -1 + 5 = 4 1 + -6k = 7[4 + 4k + -1k] Combine like terms: 4k + -1k = 3k 1 + -6k = 7[4 + 3k] 1 + -6k = [4 * 7 + 3k * 7] 1 + -6k = [28 + 21k] Solving 1 + -6k = 28 + 21k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-21k' to each side of the equation. 1 + -6k + -21k = 28 + 21k + -21k Combine like terms: -6k + -21k = -27k 1 + -27k = 28 + 21k + -21k Combine like terms: 21k + -21k = 0 1 + -27k = 28 + 0 1 + -27k = 28 Add '-1' to each side of the equation. 1 + -1 + -27k = 28 + -1 Combine like terms: 1 + -1 = 0 0 + -27k = 28 + -1 -27k = 28 + -1 Combine like terms: 28 + -1 = 27 -27k = 27 Divide each side by '-27'. k = -1 Simplifying k = -1
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