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Simplifying 2[5(w + 3) + -1(w + 1)] = 3(1 + w) Reorder the terms: 2[5(3 + w) + -1(w + 1)] = 3(1 + w) 2[(3 * 5 + w * 5) + -1(w + 1)] = 3(1 + w) 2[(15 + 5w) + -1(w + 1)] = 3(1 + w) Reorder the terms: 2[15 + 5w + -1(1 + w)] = 3(1 + w) 2[15 + 5w + (1 * -1 + w * -1)] = 3(1 + w) 2[15 + 5w + (-1 + -1w)] = 3(1 + w) Reorder the terms: 2[15 + -1 + 5w + -1w] = 3(1 + w) Combine like terms: 15 + -1 = 14 2[14 + 5w + -1w] = 3(1 + w) Combine like terms: 5w + -1w = 4w 2[14 + 4w] = 3(1 + w) [14 * 2 + 4w * 2] = 3(1 + w) [28 + 8w] = 3(1 + w) 28 + 8w = (1 * 3 + w * 3) 28 + 8w = (3 + 3w) Solving 28 + 8w = 3 + 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. 28 + 8w + -3w = 3 + 3w + -3w Combine like terms: 8w + -3w = 5w 28 + 5w = 3 + 3w + -3w Combine like terms: 3w + -3w = 0 28 + 5w = 3 + 0 28 + 5w = 3 Add '-28' to each side of the equation. 28 + -28 + 5w = 3 + -28 Combine like terms: 28 + -28 = 0 0 + 5w = 3 + -28 5w = 3 + -28 Combine like terms: 3 + -28 = -25 5w = -25 Divide each side by '5'. w = -5 Simplifying w = -5
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