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Simplifying 3(4k + -1) + 2(5k + -3k) = 7k + 6 Reorder the terms: 3(-1 + 4k) + 2(5k + -3k) = 7k + 6 (-1 * 3 + 4k * 3) + 2(5k + -3k) = 7k + 6 (-3 + 12k) + 2(5k + -3k) = 7k + 6 Combine like terms: 5k + -3k = 2k -3 + 12k + 2(2k) = 7k + 6 Remove parenthesis around (2k) -3 + 12k + 2 * 2k = 7k + 6 Multiply 2 * 2 -3 + 12k + 4k = 7k + 6 Combine like terms: 12k + 4k = 16k -3 + 16k = 7k + 6 Reorder the terms: -3 + 16k = 6 + 7k Solving -3 + 16k = 6 + 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 + 16k + -7k = 6 + 7k + -7k Combine like terms: 16k + -7k = 9k -3 + 9k = 6 + 7k + -7k Combine like terms: 7k + -7k = 0 -3 + 9k = 6 + 0 -3 + 9k = 6 Add '3' to each side of the equation. -3 + 3 + 9k = 6 + 3 Combine like terms: -3 + 3 = 0 0 + 9k = 6 + 3 9k = 6 + 3 Combine like terms: 6 + 3 = 9 9k = 9 Divide each side by '9'. k = 1 Simplifying k = 1
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