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Simplifying -31 + -6k = 1 + -5(k + 7) Reorder the terms: -31 + -6k = 1 + -5(7 + k) -31 + -6k = 1 + (7 * -5 + k * -5) -31 + -6k = 1 + (-35 + -5k) Combine like terms: 1 + -35 = -34 -31 + -6k = -34 + -5k Solving -31 + -6k = -34 + -5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5k' to each side of the equation. -31 + -6k + 5k = -34 + -5k + 5k Combine like terms: -6k + 5k = -1k -31 + -1k = -34 + -5k + 5k Combine like terms: -5k + 5k = 0 -31 + -1k = -34 + 0 -31 + -1k = -34 Add '31' to each side of the equation. -31 + 31 + -1k = -34 + 31 Combine like terms: -31 + 31 = 0 0 + -1k = -34 + 31 -1k = -34 + 31 Combine like terms: -34 + 31 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3
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