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Simplifying 7(3 + -2k) + 9(k + -5) = 0 (3 * 7 + -2k * 7) + 9(k + -5) = 0 (21 + -14k) + 9(k + -5) = 0 Reorder the terms: 21 + -14k + 9(-5 + k) = 0 21 + -14k + (-5 * 9 + k * 9) = 0 21 + -14k + (-45 + 9k) = 0 Reorder the terms: 21 + -45 + -14k + 9k = 0 Combine like terms: 21 + -45 = -24 -24 + -14k + 9k = 0 Combine like terms: -14k + 9k = -5k -24 + -5k = 0 Solving -24 + -5k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -5k = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -5k = 0 + 24 -5k = 0 + 24 Combine like terms: 0 + 24 = 24 -5k = 24 Divide each side by '-5'. k = -4.8 Simplifying k = -4.8
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