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Simplifying -5(7 + -3k) + 8 = -5k + -3(-7k + 1) (7 * -5 + -3k * -5) + 8 = -5k + -3(-7k + 1) (-35 + 15k) + 8 = -5k + -3(-7k + 1) Reorder the terms: -35 + 8 + 15k = -5k + -3(-7k + 1) Combine like terms: -35 + 8 = -27 -27 + 15k = -5k + -3(-7k + 1) Reorder the terms: -27 + 15k = -5k + -3(1 + -7k) -27 + 15k = -5k + (1 * -3 + -7k * -3) -27 + 15k = -5k + (-3 + 21k) Reorder the terms: -27 + 15k = -3 + -5k + 21k Combine like terms: -5k + 21k = 16k -27 + 15k = -3 + 16k Solving -27 + 15k = -3 + 16k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-16k' to each side of the equation. -27 + 15k + -16k = -3 + 16k + -16k Combine like terms: 15k + -16k = -1k -27 + -1k = -3 + 16k + -16k Combine like terms: 16k + -16k = 0 -27 + -1k = -3 + 0 -27 + -1k = -3 Add '27' to each side of the equation. -27 + 27 + -1k = -3 + 27 Combine like terms: -27 + 27 = 0 0 + -1k = -3 + 27 -1k = -3 + 27 Combine like terms: -3 + 27 = 24 -1k = 24 Divide each side by '-1'. k = -24 Simplifying k = -24
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