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Simplifying -5[(9k + 6) + -1(8k + -1)] = 9(5 + -1k) + -5 Reorder the terms: -5[(6 + 9k) + -1(8k + -1)] = 9(5 + -1k) + -5 Remove parenthesis around (6 + 9k) -5[6 + 9k + -1(8k + -1)] = 9(5 + -1k) + -5 Reorder the terms: -5[6 + 9k + -1(-1 + 8k)] = 9(5 + -1k) + -5 -5[6 + 9k + (-1 * -1 + 8k * -1)] = 9(5 + -1k) + -5 -5[6 + 9k + (1 + -8k)] = 9(5 + -1k) + -5 Reorder the terms: -5[6 + 1 + 9k + -8k] = 9(5 + -1k) + -5 Combine like terms: 6 + 1 = 7 -5[7 + 9k + -8k] = 9(5 + -1k) + -5 Combine like terms: 9k + -8k = 1k -5[7 + 1k] = 9(5 + -1k) + -5 [7 * -5 + 1k * -5] = 9(5 + -1k) + -5 [-35 + -5k] = 9(5 + -1k) + -5 -35 + -5k = (5 * 9 + -1k * 9) + -5 -35 + -5k = (45 + -9k) + -5 Reorder the terms: -35 + -5k = 45 + -5 + -9k Combine like terms: 45 + -5 = 40 -35 + -5k = 40 + -9k Solving -35 + -5k = 40 + -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. -35 + -5k + 9k = 40 + -9k + 9k Combine like terms: -5k + 9k = 4k -35 + 4k = 40 + -9k + 9k Combine like terms: -9k + 9k = 0 -35 + 4k = 40 + 0 -35 + 4k = 40 Add '35' to each side of the equation. -35 + 35 + 4k = 40 + 35 Combine like terms: -35 + 35 = 0 0 + 4k = 40 + 35 4k = 40 + 35 Combine like terms: 40 + 35 = 75 4k = 75 Divide each side by '4'. k = 18.75 Simplifying k = 18.75
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