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Simplifying 5k + -3(4k + 1) = 5(3 + -1k) Reorder the terms: 5k + -3(1 + 4k) = 5(3 + -1k) 5k + (1 * -3 + 4k * -3) = 5(3 + -1k) 5k + (-3 + -12k) = 5(3 + -1k) Reorder the terms: -3 + 5k + -12k = 5(3 + -1k) Combine like terms: 5k + -12k = -7k -3 + -7k = 5(3 + -1k) -3 + -7k = (3 * 5 + -1k * 5) -3 + -7k = (15 + -5k) Solving -3 + -7k = 15 + -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. -3 + -7k + 5k = 15 + -5k + 5k Combine like terms: -7k + 5k = -2k -3 + -2k = 15 + -5k + 5k Combine like terms: -5k + 5k = 0 -3 + -2k = 15 + 0 -3 + -2k = 15 Add '3' to each side of the equation. -3 + 3 + -2k = 15 + 3 Combine like terms: -3 + 3 = 0 0 + -2k = 15 + 3 -2k = 15 + 3 Combine like terms: 15 + 3 = 18 -2k = 18 Divide each side by '-2'. k = -9 Simplifying k = -9
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