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Simplifying -2(1 + 4k) + -7(k + 1) = 66 (1 * -2 + 4k * -2) + -7(k + 1) = 66 (-2 + -8k) + -7(k + 1) = 66 Reorder the terms: -2 + -8k + -7(1 + k) = 66 -2 + -8k + (1 * -7 + k * -7) = 66 -2 + -8k + (-7 + -7k) = 66 Reorder the terms: -2 + -7 + -8k + -7k = 66 Combine like terms: -2 + -7 = -9 -9 + -8k + -7k = 66 Combine like terms: -8k + -7k = -15k -9 + -15k = 66 Solving -9 + -15k = 66 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -15k = 66 + 9 Combine like terms: -9 + 9 = 0 0 + -15k = 66 + 9 -15k = 66 + 9 Combine like terms: 66 + 9 = 75 -15k = 75 Divide each side by '-15'. k = -5 Simplifying k = -5
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