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Simplifying 2(w + -4w + 7) + 1 = 2(w + 6) Reorder the terms: 2(7 + w + -4w) + 1 = 2(w + 6) Combine like terms: w + -4w = -3w 2(7 + -3w) + 1 = 2(w + 6) (7 * 2 + -3w * 2) + 1 = 2(w + 6) (14 + -6w) + 1 = 2(w + 6) Reorder the terms: 14 + 1 + -6w = 2(w + 6) Combine like terms: 14 + 1 = 15 15 + -6w = 2(w + 6) Reorder the terms: 15 + -6w = 2(6 + w) 15 + -6w = (6 * 2 + w * 2) 15 + -6w = (12 + 2w) Solving 15 + -6w = 12 + 2w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2w' to each side of the equation. 15 + -6w + -2w = 12 + 2w + -2w Combine like terms: -6w + -2w = -8w 15 + -8w = 12 + 2w + -2w Combine like terms: 2w + -2w = 0 15 + -8w = 12 + 0 15 + -8w = 12 Add '-15' to each side of the equation. 15 + -15 + -8w = 12 + -15 Combine like terms: 15 + -15 = 0 0 + -8w = 12 + -15 -8w = 12 + -15 Combine like terms: 12 + -15 = -3 -8w = -3 Divide each side by '-8'. w = 0.375 Simplifying w = 0.375
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