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Simplifying 6(4 + -3k) = 42 + 9k (4 * 6 + -3k * 6) = 42 + 9k (24 + -18k) = 42 + 9k Solving 24 + -18k = 42 + 9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9k' to each side of the equation. 24 + -18k + -9k = 42 + 9k + -9k Combine like terms: -18k + -9k = -27k 24 + -27k = 42 + 9k + -9k Combine like terms: 9k + -9k = 0 24 + -27k = 42 + 0 24 + -27k = 42 Add '-24' to each side of the equation. 24 + -24 + -27k = 42 + -24 Combine like terms: 24 + -24 = 0 0 + -27k = 42 + -24 -27k = 42 + -24 Combine like terms: 42 + -24 = 18 -27k = 18 Divide each side by '-27'. k = -0.6666666667 Simplifying k = -0.6666666667
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