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Simplifying 2 + 4(3w + -2) + -3(2w + -4w + -4) + 8w = 45 Reorder the terms: 2 + 4(-2 + 3w) + -3(2w + -4w + -4) + 8w = 45 2 + (-2 * 4 + 3w * 4) + -3(2w + -4w + -4) + 8w = 45 2 + (-8 + 12w) + -3(2w + -4w + -4) + 8w = 45 Reorder the terms: 2 + -8 + 12w + -3(-4 + 2w + -4w) + 8w = 45 Combine like terms: 2w + -4w = -2w 2 + -8 + 12w + -3(-4 + -2w) + 8w = 45 2 + -8 + 12w + (-4 * -3 + -2w * -3) + 8w = 45 2 + -8 + 12w + (12 + 6w) + 8w = 45 Reorder the terms: 2 + -8 + 12 + 12w + 6w + 8w = 45 Combine like terms: 2 + -8 = -6 -6 + 12 + 12w + 6w + 8w = 45 Combine like terms: -6 + 12 = 6 6 + 12w + 6w + 8w = 45 Combine like terms: 12w + 6w = 18w 6 + 18w + 8w = 45 Combine like terms: 18w + 8w = 26w 6 + 26w = 45 Solving 6 + 26w = 45 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 26w = 45 + -6 Combine like terms: 6 + -6 = 0 0 + 26w = 45 + -6 26w = 45 + -6 Combine like terms: 45 + -6 = 39 26w = 39 Divide each side by '26'. w = 1.5 Simplifying w = 1.5
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