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Simplifying 7w + 3(3 + -2w) = 4(w + 2) + -1(2w + -9) 7w + (3 * 3 + -2w * 3) = 4(w + 2) + -1(2w + -9) 7w + (9 + -6w) = 4(w + 2) + -1(2w + -9) Reorder the terms: 9 + 7w + -6w = 4(w + 2) + -1(2w + -9) Combine like terms: 7w + -6w = 1w 9 + 1w = 4(w + 2) + -1(2w + -9) Reorder the terms: 9 + 1w = 4(2 + w) + -1(2w + -9) 9 + 1w = (2 * 4 + w * 4) + -1(2w + -9) 9 + 1w = (8 + 4w) + -1(2w + -9) Reorder the terms: 9 + 1w = 8 + 4w + -1(-9 + 2w) 9 + 1w = 8 + 4w + (-9 * -1 + 2w * -1) 9 + 1w = 8 + 4w + (9 + -2w) Reorder the terms: 9 + 1w = 8 + 9 + 4w + -2w Combine like terms: 8 + 9 = 17 9 + 1w = 17 + 4w + -2w Combine like terms: 4w + -2w = 2w 9 + 1w = 17 + 2w Solving 9 + 1w = 17 + 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. 9 + 1w + -2w = 17 + 2w + -2w Combine like terms: 1w + -2w = -1w 9 + -1w = 17 + 2w + -2w Combine like terms: 2w + -2w = 0 9 + -1w = 17 + 0 9 + -1w = 17 Add '-9' to each side of the equation. 9 + -9 + -1w = 17 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 17 + -9 -1w = 17 + -9 Combine like terms: 17 + -9 = 8 -1w = 8 Divide each side by '-1'. w = -8 Simplifying w = -8
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