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Simplifying (3w + -8) + -1(4 + -9w) + 3 = 7w + -2 + -1(5w + 9 + -3) Reorder the terms: (-8 + 3w) + -1(4 + -9w) + 3 = 7w + -2 + -1(5w + 9 + -3) Remove parenthesis around (-8 + 3w) -8 + 3w + -1(4 + -9w) + 3 = 7w + -2 + -1(5w + 9 + -3) -8 + 3w + (4 * -1 + -9w * -1) + 3 = 7w + -2 + -1(5w + 9 + -3) -8 + 3w + (-4 + 9w) + 3 = 7w + -2 + -1(5w + 9 + -3) Reorder the terms: -8 + -4 + 3 + 3w + 9w = 7w + -2 + -1(5w + 9 + -3) Combine like terms: -8 + -4 = -12 -12 + 3 + 3w + 9w = 7w + -2 + -1(5w + 9 + -3) Combine like terms: -12 + 3 = -9 -9 + 3w + 9w = 7w + -2 + -1(5w + 9 + -3) Combine like terms: 3w + 9w = 12w -9 + 12w = 7w + -2 + -1(5w + 9 + -3) Reorder the terms: -9 + 12w = 7w + -2 + -1(9 + -3 + 5w) Combine like terms: 9 + -3 = 6 -9 + 12w = 7w + -2 + -1(6 + 5w) -9 + 12w = 7w + -2 + (6 * -1 + 5w * -1) -9 + 12w = 7w + -2 + (-6 + -5w) Reorder the terms: -9 + 12w = -2 + -6 + 7w + -5w Combine like terms: -2 + -6 = -8 -9 + 12w = -8 + 7w + -5w Combine like terms: 7w + -5w = 2w -9 + 12w = -8 + 2w Solving -9 + 12w = -8 + 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 = -8 + 2w + -2w Combine like terms: 12w + -2w = 10w -9 + 10w = -8 + 2w + -2w Combine like terms: 2w + -2w = 0 -9 + 10w = -8 + 0 -9 + 10w = -8 Add '9' to each side of the equation. -9 + 9 + 10w = -8 + 9 Combine like terms: -9 + 9 = 0 0 + 10w = -8 + 9 10w = -8 + 9 Combine like terms: -8 + 9 = 1 10w = 1 Divide each side by '10'. w = 0.1 Simplifying w = 0.1
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