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Simplifying w + -2[w + 5(1 + -2w) + 4w] + -1(w + 3) = -1w + 3(w + 2) + 7w w + -2[w + (1 * 5 + -2w * 5) + 4w] + -1(w + 3) = -1w + 3(w + 2) + 7w w + -2[w + (5 + -10w) + 4w] + -1(w + 3) = -1w + 3(w + 2) + 7w Reorder the terms: w + -2[5 + w + -10w + 4w] + -1(w + 3) = -1w + 3(w + 2) + 7w Combine like terms: w + -10w = -9w w + -2[5 + -9w + 4w] + -1(w + 3) = -1w + 3(w + 2) + 7w Combine like terms: -9w + 4w = -5w w + -2[5 + -5w] + -1(w + 3) = -1w + 3(w + 2) + 7w w + [5 * -2 + -5w * -2] + -1(w + 3) = -1w + 3(w + 2) + 7w w + [-10 + 10w] + -1(w + 3) = -1w + 3(w + 2) + 7w Reorder the terms: w + -10 + 10w + -1(3 + w) = -1w + 3(w + 2) + 7w w + -10 + 10w + (3 * -1 + w * -1) = -1w + 3(w + 2) + 7w w + -10 + 10w + (-3 + -1w) = -1w + 3(w + 2) + 7w Reorder the terms: -10 + -3 + w + 10w + -1w = -1w + 3(w + 2) + 7w Combine like terms: -10 + -3 = -13 -13 + w + 10w + -1w = -1w + 3(w + 2) + 7w Combine like terms: w + 10w = 11w -13 + 11w + -1w = -1w + 3(w + 2) + 7w Combine like terms: 11w + -1w = 10w -13 + 10w = -1w + 3(w + 2) + 7w Reorder the terms: -13 + 10w = -1w + 3(2 + w) + 7w -13 + 10w = -1w + (2 * 3 + w * 3) + 7w -13 + 10w = -1w + (6 + 3w) + 7w Reorder the terms: -13 + 10w = 6 + -1w + 3w + 7w Combine like terms: -1w + 3w = 2w -13 + 10w = 6 + 2w + 7w Combine like terms: 2w + 7w = 9w -13 + 10w = 6 + 9w Solving -13 + 10w = 6 + 9w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9w' to each side of the equation. -13 + 10w + -9w = 6 + 9w + -9w Combine like terms: 10w + -9w = 1w -13 + 1w = 6 + 9w + -9w Combine like terms: 9w + -9w = 0 -13 + 1w = 6 + 0 -13 + 1w = 6 Add '13' to each side of the equation. -13 + 13 + 1w = 6 + 13 Combine like terms: -13 + 13 = 0 0 + 1w = 6 + 13 1w = 6 + 13 Combine like terms: 6 + 13 = 19 1w = 19 Divide each side by '1'. w = 19 Simplifying w = 19
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