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Simplifying -2[(4k + 1) + -1(8k + -5)] = 7(4 + -1k) + -7 Reorder the terms: -2[(1 + 4k) + -1(8k + -5)] = 7(4 + -1k) + -7 Remove parenthesis around (1 + 4k) -2[1 + 4k + -1(8k + -5)] = 7(4 + -1k) + -7 Reorder the terms: -2[1 + 4k + -1(-5 + 8k)] = 7(4 + -1k) + -7 -2[1 + 4k + (-5 * -1 + 8k * -1)] = 7(4 + -1k) + -7 -2[1 + 4k + (5 + -8k)] = 7(4 + -1k) + -7 Reorder the terms: -2[1 + 5 + 4k + -8k] = 7(4 + -1k) + -7 Combine like terms: 1 + 5 = 6 -2[6 + 4k + -8k] = 7(4 + -1k) + -7 Combine like terms: 4k + -8k = -4k -2[6 + -4k] = 7(4 + -1k) + -7 [6 * -2 + -4k * -2] = 7(4 + -1k) + -7 [-12 + 8k] = 7(4 + -1k) + -7 -12 + 8k = (4 * 7 + -1k * 7) + -7 -12 + 8k = (28 + -7k) + -7 Reorder the terms: -12 + 8k = 28 + -7 + -7k Combine like terms: 28 + -7 = 21 -12 + 8k = 21 + -7k Solving -12 + 8k = 21 + -7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7k' to each side of the equation. -12 + 8k + 7k = 21 + -7k + 7k Combine like terms: 8k + 7k = 15k -12 + 15k = 21 + -7k + 7k Combine like terms: -7k + 7k = 0 -12 + 15k = 21 + 0 -12 + 15k = 21 Add '12' to each side of the equation. -12 + 12 + 15k = 21 + 12 Combine like terms: -12 + 12 = 0 0 + 15k = 21 + 12 15k = 21 + 12 Combine like terms: 21 + 12 = 33 15k = 33 Divide each side by '15'. k = 2.2 Simplifying k = 2.2
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