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Simplifying 2(w + 17) + 5w + -1 = 2(w + 2) + 3(w + 5) Reorder the terms: 2(17 + w) + 5w + -1 = 2(w + 2) + 3(w + 5) (17 * 2 + w * 2) + 5w + -1 = 2(w + 2) + 3(w + 5) (34 + 2w) + 5w + -1 = 2(w + 2) + 3(w + 5) Reorder the terms: 34 + -1 + 2w + 5w = 2(w + 2) + 3(w + 5) Combine like terms: 34 + -1 = 33 33 + 2w + 5w = 2(w + 2) + 3(w + 5) Combine like terms: 2w + 5w = 7w 33 + 7w = 2(w + 2) + 3(w + 5) Reorder the terms: 33 + 7w = 2(2 + w) + 3(w + 5) 33 + 7w = (2 * 2 + w * 2) + 3(w + 5) 33 + 7w = (4 + 2w) + 3(w + 5) Reorder the terms: 33 + 7w = 4 + 2w + 3(5 + w) 33 + 7w = 4 + 2w + (5 * 3 + w * 3) 33 + 7w = 4 + 2w + (15 + 3w) Reorder the terms: 33 + 7w = 4 + 15 + 2w + 3w Combine like terms: 4 + 15 = 19 33 + 7w = 19 + 2w + 3w Combine like terms: 2w + 3w = 5w 33 + 7w = 19 + 5w Solving 33 + 7w = 19 + 5w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5w' to each side of the equation. 33 + 7w + -5w = 19 + 5w + -5w Combine like terms: 7w + -5w = 2w 33 + 2w = 19 + 5w + -5w Combine like terms: 5w + -5w = 0 33 + 2w = 19 + 0 33 + 2w = 19 Add '-33' to each side of the equation. 33 + -33 + 2w = 19 + -33 Combine like terms: 33 + -33 = 0 0 + 2w = 19 + -33 2w = 19 + -33 Combine like terms: 19 + -33 = -14 2w = -14 Divide each side by '2'. w = -7 Simplifying w = -7
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