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Simplifying 3(w + -5) + -2(1 + -1w) = 3(4 + -1w) Reorder the terms: 3(-5 + w) + -2(1 + -1w) = 3(4 + -1w) (-5 * 3 + w * 3) + -2(1 + -1w) = 3(4 + -1w) (-15 + 3w) + -2(1 + -1w) = 3(4 + -1w) -15 + 3w + (1 * -2 + -1w * -2) = 3(4 + -1w) -15 + 3w + (-2 + 2w) = 3(4 + -1w) Reorder the terms: -15 + -2 + 3w + 2w = 3(4 + -1w) Combine like terms: -15 + -2 = -17 -17 + 3w + 2w = 3(4 + -1w) Combine like terms: 3w + 2w = 5w -17 + 5w = 3(4 + -1w) -17 + 5w = (4 * 3 + -1w * 3) -17 + 5w = (12 + -3w) Solving -17 + 5w = 12 + -3w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3w' to each side of the equation. -17 + 5w + 3w = 12 + -3w + 3w Combine like terms: 5w + 3w = 8w -17 + 8w = 12 + -3w + 3w Combine like terms: -3w + 3w = 0 -17 + 8w = 12 + 0 -17 + 8w = 12 Add '17' to each side of the equation. -17 + 17 + 8w = 12 + 17 Combine like terms: -17 + 17 = 0 0 + 8w = 12 + 17 8w = 12 + 17 Combine like terms: 12 + 17 = 29 8w = 29 Divide each side by '8'. w = 3.625 Simplifying w = 3.625
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