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Simplifying -4(3 + 9k) = 6(k + 5) (3 * -4 + 9k * -4) = 6(k + 5) (-12 + -36k) = 6(k + 5) Reorder the terms: -12 + -36k = 6(5 + k) -12 + -36k = (5 * 6 + k * 6) -12 + -36k = (30 + 6k) Solving -12 + -36k = 30 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. -12 + -36k + -6k = 30 + 6k + -6k Combine like terms: -36k + -6k = -42k -12 + -42k = 30 + 6k + -6k Combine like terms: 6k + -6k = 0 -12 + -42k = 30 + 0 -12 + -42k = 30 Add '12' to each side of the equation. -12 + 12 + -42k = 30 + 12 Combine like terms: -12 + 12 = 0 0 + -42k = 30 + 12 -42k = 30 + 12 Combine like terms: 30 + 12 = 42 -42k = 42 Divide each side by '-42'. k = -1 Simplifying k = -1
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