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Simplifying (3w + -8) + -1(4 + -9w) + 3 = 7w + -2 + -1(5w + 9 + -31) Reorder the terms: (-8 + 3w) + -1(4 + -9w) + 3 = 7w + -2 + -1(5w + 9 + -31) Remove parenthesis around (-8 + 3w) -8 + 3w + -1(4 + -9w) + 3 = 7w + -2 + -1(5w + 9 + -31) -8 + 3w + (4 * -1 + -9w * -1) + 3 = 7w + -2 + -1(5w + 9 + -31) -8 + 3w + (-4 + 9w) + 3 = 7w + -2 + -1(5w + 9 + -31) Reorder the terms: -8 + -4 + 3 + 3w + 9w = 7w + -2 + -1(5w + 9 + -31) Combine like terms: -8 + -4 = -12 -12 + 3 + 3w + 9w = 7w + -2 + -1(5w + 9 + -31) Combine like terms: -12 + 3 = -9 -9 + 3w + 9w = 7w + -2 + -1(5w + 9 + -31) Combine like terms: 3w + 9w = 12w -9 + 12w = 7w + -2 + -1(5w + 9 + -31) Reorder the terms: -9 + 12w = 7w + -2 + -1(9 + -31 + 5w) Combine like terms: 9 + -31 = -22 -9 + 12w = 7w + -2 + -1(-22 + 5w) -9 + 12w = 7w + -2 + (-22 * -1 + 5w * -1) -9 + 12w = 7w + -2 + (22 + -5w) Reorder the terms: -9 + 12w = -2 + 22 + 7w + -5w Combine like terms: -2 + 22 = 20 -9 + 12w = 20 + 7w + -5w Combine like terms: 7w + -5w = 2w -9 + 12w = 20 + 2w Solving -9 + 12w = 20 + 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 + 12w + -2w = 20 + 2w + -2w Combine like terms: 12w + -2w = 10w -9 + 10w = 20 + 2w + -2w Combine like terms: 2w + -2w = 0 -9 + 10w = 20 + 0 -9 + 10w = 20 Add '9' to each side of the equation. -9 + 9 + 10w = 20 + 9 Combine like terms: -9 + 9 = 0 0 + 10w = 20 + 9 10w = 20 + 9 Combine like terms: 20 + 9 = 29 10w = 29 Divide each side by '10'. w = 2.9 Simplifying w = 2.9
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