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Simplifying 27 + -3(2w + 1) = 12w + -3(12 + w) Reorder the terms: 27 + -3(1 + 2w) = 12w + -3(12 + w) 27 + (1 * -3 + 2w * -3) = 12w + -3(12 + w) 27 + (-3 + -6w) = 12w + -3(12 + w) Combine like terms: 27 + -3 = 24 24 + -6w = 12w + -3(12 + w) 24 + -6w = 12w + (12 * -3 + w * -3) 24 + -6w = 12w + (-36 + -3w) Reorder the terms: 24 + -6w = -36 + 12w + -3w Combine like terms: 12w + -3w = 9w 24 + -6w = -36 + 9w Solving 24 + -6w = -36 + 9w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9w' to each side of the equation. 24 + -6w + -9w = -36 + 9w + -9w Combine like terms: -6w + -9w = -15w 24 + -15w = -36 + 9w + -9w Combine like terms: 9w + -9w = 0 24 + -15w = -36 + 0 24 + -15w = -36 Add '-24' to each side of the equation. 24 + -24 + -15w = -36 + -24 Combine like terms: 24 + -24 = 0 0 + -15w = -36 + -24 -15w = -36 + -24 Combine like terms: -36 + -24 = -60 -15w = -60 Divide each side by '-15'. w = 4 Simplifying w = 4
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