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Simplifying -5(k + 8) + -1(2 + 7k) = -13k Reorder the terms: -5(8 + k) + -1(2 + 7k) = -13k (8 * -5 + k * -5) + -1(2 + 7k) = -13k (-40 + -5k) + -1(2 + 7k) = -13k -40 + -5k + (2 * -1 + 7k * -1) = -13k -40 + -5k + (-2 + -7k) = -13k Reorder the terms: -40 + -2 + -5k + -7k = -13k Combine like terms: -40 + -2 = -42 -42 + -5k + -7k = -13k Combine like terms: -5k + -7k = -12k -42 + -12k = -13k Solving -42 + -12k = -13k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '13k' to each side of the equation. -42 + -12k + 13k = -13k + 13k Combine like terms: -12k + 13k = 1k -42 + 1k = -13k + 13k Combine like terms: -13k + 13k = 0 -42 + 1k = 0 Add '42' to each side of the equation. -42 + 42 + 1k = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 1k = 0 + 42 1k = 0 + 42 Combine like terms: 0 + 42 = 42 1k = 42 Divide each side by '1'. k = 42 Simplifying k = 42
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