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Simplifying 2(3w + 1) = 2w + 1 + 7 + w Reorder the terms: 2(1 + 3w) = 2w + 1 + 7 + w (1 * 2 + 3w * 2) = 2w + 1 + 7 + w (2 + 6w) = 2w + 1 + 7 + w Reorder the terms: 2 + 6w = 1 + 7 + 2w + w Combine like terms: 1 + 7 = 8 2 + 6w = 8 + 2w + w Combine like terms: 2w + w = 3w 2 + 6w = 8 + 3w Solving 2 + 6w = 8 + 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. 2 + 6w + -3w = 8 + 3w + -3w Combine like terms: 6w + -3w = 3w 2 + 3w = 8 + 3w + -3w Combine like terms: 3w + -3w = 0 2 + 3w = 8 + 0 2 + 3w = 8 Add '-2' to each side of the equation. 2 + -2 + 3w = 8 + -2 Combine like terms: 2 + -2 = 0 0 + 3w = 8 + -2 3w = 8 + -2 Combine like terms: 8 + -2 = 6 3w = 6 Divide each side by '3'. w = 2 Simplifying w = 2
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