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Simplifying 5(1 + -4k) + 7k = -5k + -35 (1 * 5 + -4k * 5) + 7k = -5k + -35 (5 + -20k) + 7k = -5k + -35 Combine like terms: -20k + 7k = -13k 5 + -13k = -5k + -35 Reorder the terms: 5 + -13k = -35 + -5k Solving 5 + -13k = -35 + -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. 5 + -13k + 5k = -35 + -5k + 5k Combine like terms: -13k + 5k = -8k 5 + -8k = -35 + -5k + 5k Combine like terms: -5k + 5k = 0 5 + -8k = -35 + 0 5 + -8k = -35 Add '-5' to each side of the equation. 5 + -5 + -8k = -35 + -5 Combine like terms: 5 + -5 = 0 0 + -8k = -35 + -5 -8k = -35 + -5 Combine like terms: -35 + -5 = -40 -8k = -40 Divide each side by '-8'. k = 5 Simplifying k = 5
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