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Simplifying 2 + -5(1 + -3k) = 5 + 7k 2 + (1 * -5 + -3k * -5) = 5 + 7k 2 + (-5 + 15k) = 5 + 7k Combine like terms: 2 + -5 = -3 -3 + 15k = 5 + 7k Solving -3 + 15k = 5 + 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. -3 + 15k + -7k = 5 + 7k + -7k Combine like terms: 15k + -7k = 8k -3 + 8k = 5 + 7k + -7k Combine like terms: 7k + -7k = 0 -3 + 8k = 5 + 0 -3 + 8k = 5 Add '3' to each side of the equation. -3 + 3 + 8k = 5 + 3 Combine like terms: -3 + 3 = 0 0 + 8k = 5 + 3 8k = 5 + 3 Combine like terms: 5 + 3 = 8 8k = 8 Divide each side by '8'. k = 1 Simplifying k = 1
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