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Simplifying -7(-5k + 3) + -1 = 6k + 7 Reorder the terms: -7(3 + -5k) + -1 = 6k + 7 (3 * -7 + -5k * -7) + -1 = 6k + 7 (-21 + 35k) + -1 = 6k + 7 Reorder the terms: -21 + -1 + 35k = 6k + 7 Combine like terms: -21 + -1 = -22 -22 + 35k = 6k + 7 Reorder the terms: -22 + 35k = 7 + 6k Solving -22 + 35k = 7 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. -22 + 35k + -6k = 7 + 6k + -6k Combine like terms: 35k + -6k = 29k -22 + 29k = 7 + 6k + -6k Combine like terms: 6k + -6k = 0 -22 + 29k = 7 + 0 -22 + 29k = 7 Add '22' to each side of the equation. -22 + 22 + 29k = 7 + 22 Combine like terms: -22 + 22 = 0 0 + 29k = 7 + 22 29k = 7 + 22 Combine like terms: 7 + 22 = 29 29k = 29 Divide each side by '29'. k = 1 Simplifying k = 1
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