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Simplifying 31 + -4(2w + 1) = 7w + -4(7 + w) Reorder the terms: 31 + -4(1 + 2w) = 7w + -4(7 + w) 31 + (1 * -4 + 2w * -4) = 7w + -4(7 + w) 31 + (-4 + -8w) = 7w + -4(7 + w) Combine like terms: 31 + -4 = 27 27 + -8w = 7w + -4(7 + w) 27 + -8w = 7w + (7 * -4 + w * -4) 27 + -8w = 7w + (-28 + -4w) Reorder the terms: 27 + -8w = -28 + 7w + -4w Combine like terms: 7w + -4w = 3w 27 + -8w = -28 + 3w Solving 27 + -8w = -28 + 3w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3w' to each side of the equation. 27 + -8w + -3w = -28 + 3w + -3w Combine like terms: -8w + -3w = -11w 27 + -11w = -28 + 3w + -3w Combine like terms: 3w + -3w = 0 27 + -11w = -28 + 0 27 + -11w = -28 Add '-27' to each side of the equation. 27 + -27 + -11w = -28 + -27 Combine like terms: 27 + -27 = 0 0 + -11w = -28 + -27 -11w = -28 + -27 Combine like terms: -28 + -27 = -55 -11w = -55 Divide each side by '-11'. w = 5 Simplifying w = 5
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