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