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Simplifying 17 = 5(-7 + -4k) + 4(1 + 8k) 17 = (-7 * 5 + -4k * 5) + 4(1 + 8k) 17 = (-35 + -20k) + 4(1 + 8k) 17 = -35 + -20k + (1 * 4 + 8k * 4) 17 = -35 + -20k + (4 + 32k) Reorder the terms: 17 = -35 + 4 + -20k + 32k Combine like terms: -35 + 4 = -31 17 = -31 + -20k + 32k Combine like terms: -20k + 32k = 12k 17 = -31 + 12k Solving 17 = -31 + 12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12k' to each side of the equation. 17 + -12k = -31 + 12k + -12k Combine like terms: 12k + -12k = 0 17 + -12k = -31 + 0 17 + -12k = -31 Add '-17' to each side of the equation. 17 + -17 + -12k = -31 + -17 Combine like terms: 17 + -17 = 0 0 + -12k = -31 + -17 -12k = -31 + -17 Combine like terms: -31 + -17 = -48 -12k = -48 Divide each side by '-12'. k = 4 Simplifying k = 4
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