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Simplifying -6 + -7(5k + -7) = 3k + -11(1 + 4k) Reorder the terms: -6 + -7(-7 + 5k) = 3k + -11(1 + 4k) -6 + (-7 * -7 + 5k * -7) = 3k + -11(1 + 4k) -6 + (49 + -35k) = 3k + -11(1 + 4k) Combine like terms: -6 + 49 = 43 43 + -35k = 3k + -11(1 + 4k) 43 + -35k = 3k + (1 * -11 + 4k * -11) 43 + -35k = 3k + (-11 + -44k) Reorder the terms: 43 + -35k = -11 + 3k + -44k Combine like terms: 3k + -44k = -41k 43 + -35k = -11 + -41k Solving 43 + -35k = -11 + -41k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '41k' to each side of the equation. 43 + -35k + 41k = -11 + -41k + 41k Combine like terms: -35k + 41k = 6k 43 + 6k = -11 + -41k + 41k Combine like terms: -41k + 41k = 0 43 + 6k = -11 + 0 43 + 6k = -11 Add '-43' to each side of the equation. 43 + -43 + 6k = -11 + -43 Combine like terms: 43 + -43 = 0 0 + 6k = -11 + -43 6k = -11 + -43 Combine like terms: -11 + -43 = -54 6k = -54 Divide each side by '6'. k = -9 Simplifying k = -9
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