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Simplifying 3(3k + -1) = 4(4k + 1) Reorder the terms: 3(-1 + 3k) = 4(4k + 1) (-1 * 3 + 3k * 3) = 4(4k + 1) (-3 + 9k) = 4(4k + 1) Reorder the terms: -3 + 9k = 4(1 + 4k) -3 + 9k = (1 * 4 + 4k * 4) -3 + 9k = (4 + 16k) Solving -3 + 9k = 4 + 16k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-16k' to each side of the equation. -3 + 9k + -16k = 4 + 16k + -16k Combine like terms: 9k + -16k = -7k -3 + -7k = 4 + 16k + -16k Combine like terms: 16k + -16k = 0 -3 + -7k = 4 + 0 -3 + -7k = 4 Add '3' to each side of the equation. -3 + 3 + -7k = 4 + 3 Combine like terms: -3 + 3 = 0 0 + -7k = 4 + 3 -7k = 4 + 3 Combine like terms: 4 + 3 = 7 -7k = 7 Divide each side by '-7'. k = -1 Simplifying k = -1
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