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Simplifying 12 + -2(2w + 1) = 7w + -3(7 + w) Reorder the terms: 12 + -2(1 + 2w) = 7w + -3(7 + w) 12 + (1 * -2 + 2w * -2) = 7w + -3(7 + w) 12 + (-2 + -4w) = 7w + -3(7 + w) Combine like terms: 12 + -2 = 10 10 + -4w = 7w + -3(7 + w) 10 + -4w = 7w + (7 * -3 + w * -3) 10 + -4w = 7w + (-21 + -3w) Reorder the terms: 10 + -4w = -21 + 7w + -3w Combine like terms: 7w + -3w = 4w 10 + -4w = -21 + 4w Solving 10 + -4w = -21 + 4w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4w' to each side of the equation. 10 + -4w + -4w = -21 + 4w + -4w Combine like terms: -4w + -4w = -8w 10 + -8w = -21 + 4w + -4w Combine like terms: 4w + -4w = 0 10 + -8w = -21 + 0 10 + -8w = -21 Add '-10' to each side of the equation. 10 + -10 + -8w = -21 + -10 Combine like terms: 10 + -10 = 0 0 + -8w = -21 + -10 -8w = -21 + -10 Combine like terms: -21 + -10 = -31 -8w = -31 Divide each side by '-8'. w = 3.875 Simplifying w = 3.875
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