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Simplifying 32 + -2(2w + 1) = 11w + -2(11 + w) Reorder the terms: 32 + -2(1 + 2w) = 11w + -2(11 + w) 32 + (1 * -2 + 2w * -2) = 11w + -2(11 + w) 32 + (-2 + -4w) = 11w + -2(11 + w) Combine like terms: 32 + -2 = 30 30 + -4w = 11w + -2(11 + w) 30 + -4w = 11w + (11 * -2 + w * -2) 30 + -4w = 11w + (-22 + -2w) Reorder the terms: 30 + -4w = -22 + 11w + -2w Combine like terms: 11w + -2w = 9w 30 + -4w = -22 + 9w Solving 30 + -4w = -22 + 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. 30 + -4w + -9w = -22 + 9w + -9w Combine like terms: -4w + -9w = -13w 30 + -13w = -22 + 9w + -9w Combine like terms: 9w + -9w = 0 30 + -13w = -22 + 0 30 + -13w = -22 Add '-30' to each side of the equation. 30 + -30 + -13w = -22 + -30 Combine like terms: 30 + -30 = 0 0 + -13w = -22 + -30 -13w = -22 + -30 Combine like terms: -22 + -30 = -52 -13w = -52 Divide each side by '-13'. w = 4 Simplifying w = 4
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