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Simplifying 12k + 6(k + -9) = -6(1 + -4k) + -4k Reorder the terms: 12k + 6(-9 + k) = -6(1 + -4k) + -4k 12k + (-9 * 6 + k * 6) = -6(1 + -4k) + -4k 12k + (-54 + 6k) = -6(1 + -4k) + -4k Reorder the terms: -54 + 12k + 6k = -6(1 + -4k) + -4k Combine like terms: 12k + 6k = 18k -54 + 18k = -6(1 + -4k) + -4k -54 + 18k = (1 * -6 + -4k * -6) + -4k -54 + 18k = (-6 + 24k) + -4k Combine like terms: 24k + -4k = 20k -54 + 18k = -6 + 20k Solving -54 + 18k = -6 + 20k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-20k' to each side of the equation. -54 + 18k + -20k = -6 + 20k + -20k Combine like terms: 18k + -20k = -2k -54 + -2k = -6 + 20k + -20k Combine like terms: 20k + -20k = 0 -54 + -2k = -6 + 0 -54 + -2k = -6 Add '54' to each side of the equation. -54 + 54 + -2k = -6 + 54 Combine like terms: -54 + 54 = 0 0 + -2k = -6 + 54 -2k = -6 + 54 Combine like terms: -6 + 54 = 48 -2k = 48 Divide each side by '-2'. k = -24 Simplifying k = -24
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