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Simplifying -3(1 + 9k) + -7(-12 + 1) = 1 + 10k + -11 + -6k (1 * -3 + 9k * -3) + -7(-12 + 1) = 1 + 10k + -11 + -6k (-3 + -27k) + -7(-12 + 1) = 1 + 10k + -11 + -6k Combine like terms: -12 + 1 = -11 -3 + -27k + -7(-11) = 1 + 10k + -11 + -6k Multiply -7 * -11 -3 + -27k + 77 = 1 + 10k + -11 + -6k Reorder the terms: -3 + 77 + -27k = 1 + 10k + -11 + -6k Combine like terms: -3 + 77 = 74 74 + -27k = 1 + 10k + -11 + -6k Reorder the terms: 74 + -27k = 1 + -11 + 10k + -6k Combine like terms: 1 + -11 = -10 74 + -27k = -10 + 10k + -6k Combine like terms: 10k + -6k = 4k 74 + -27k = -10 + 4k Solving 74 + -27k = -10 + 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. 74 + -27k + -4k = -10 + 4k + -4k Combine like terms: -27k + -4k = -31k 74 + -31k = -10 + 4k + -4k Combine like terms: 4k + -4k = 0 74 + -31k = -10 + 0 74 + -31k = -10 Add '-74' to each side of the equation. 74 + -74 + -31k = -10 + -74 Combine like terms: 74 + -74 = 0 0 + -31k = -10 + -74 -31k = -10 + -74 Combine like terms: -10 + -74 = -84 -31k = -84 Divide each side by '-31'. k = 2.709677419 Simplifying k = 2.709677419
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