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Simplifying 5(5 + -1k) + -7(7 + k) = 0 (5 * 5 + -1k * 5) + -7(7 + k) = 0 (25 + -5k) + -7(7 + k) = 0 25 + -5k + (7 * -7 + k * -7) = 0 25 + -5k + (-49 + -7k) = 0 Reorder the terms: 25 + -49 + -5k + -7k = 0 Combine like terms: 25 + -49 = -24 -24 + -5k + -7k = 0 Combine like terms: -5k + -7k = -12k -24 + -12k = 0 Solving -24 + -12k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -12k = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -12k = 0 + 24 -12k = 0 + 24 Combine like terms: 0 + 24 = 24 -12k = 24 Divide each side by '-12'. k = -2 Simplifying k = -2
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