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Simplifying 3(4k + -8) + -4(5k + 7) + -9k = 0 Reorder the terms: 3(-8 + 4k) + -4(5k + 7) + -9k = 0 (-8 * 3 + 4k * 3) + -4(5k + 7) + -9k = 0 (-24 + 12k) + -4(5k + 7) + -9k = 0 Reorder the terms: -24 + 12k + -4(7 + 5k) + -9k = 0 -24 + 12k + (7 * -4 + 5k * -4) + -9k = 0 -24 + 12k + (-28 + -20k) + -9k = 0 Reorder the terms: -24 + -28 + 12k + -20k + -9k = 0 Combine like terms: -24 + -28 = -52 -52 + 12k + -20k + -9k = 0 Combine like terms: 12k + -20k = -8k -52 + -8k + -9k = 0 Combine like terms: -8k + -9k = -17k -52 + -17k = 0 Solving -52 + -17k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + -17k = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -17k = 0 + 52 -17k = 0 + 52 Combine like terms: 0 + 52 = 52 -17k = 52 Divide each side by '-17'. k = -3.058823529 Simplifying k = -3.058823529
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