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Simplifying -5[(4k + 1) + -1(5k + -6)] = 4(4 + -1k) + -4 Reorder the terms: -5[(1 + 4k) + -1(5k + -6)] = 4(4 + -1k) + -4 Remove parenthesis around (1 + 4k) -5[1 + 4k + -1(5k + -6)] = 4(4 + -1k) + -4 Reorder the terms: -5[1 + 4k + -1(-6 + 5k)] = 4(4 + -1k) + -4 -5[1 + 4k + (-6 * -1 + 5k * -1)] = 4(4 + -1k) + -4 -5[1 + 4k + (6 + -5k)] = 4(4 + -1k) + -4 Reorder the terms: -5[1 + 6 + 4k + -5k] = 4(4 + -1k) + -4 Combine like terms: 1 + 6 = 7 -5[7 + 4k + -5k] = 4(4 + -1k) + -4 Combine like terms: 4k + -5k = -1k -5[7 + -1k] = 4(4 + -1k) + -4 [7 * -5 + -1k * -5] = 4(4 + -1k) + -4 [-35 + 5k] = 4(4 + -1k) + -4 -35 + 5k = (4 * 4 + -1k * 4) + -4 -35 + 5k = (16 + -4k) + -4 Reorder the terms: -35 + 5k = 16 + -4 + -4k Combine like terms: 16 + -4 = 12 -35 + 5k = 12 + -4k Solving -35 + 5k = 12 + -4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4k' to each side of the equation. -35 + 5k + 4k = 12 + -4k + 4k Combine like terms: 5k + 4k = 9k -35 + 9k = 12 + -4k + 4k Combine like terms: -4k + 4k = 0 -35 + 9k = 12 + 0 -35 + 9k = 12 Add '35' to each side of the equation. -35 + 35 + 9k = 12 + 35 Combine like terms: -35 + 35 = 0 0 + 9k = 12 + 35 9k = 12 + 35 Combine like terms: 12 + 35 = 47 9k = 47 Divide each side by '9'. k = 5.222222222 Simplifying k = 5.222222222
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