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Simplifying 12 + -3(w + 1) = 8w + -3(8 + w) Reorder the terms: 12 + -3(1 + w) = 8w + -3(8 + w) 12 + (1 * -3 + w * -3) = 8w + -3(8 + w) 12 + (-3 + -3w) = 8w + -3(8 + w) Combine like terms: 12 + -3 = 9 9 + -3w = 8w + -3(8 + w) 9 + -3w = 8w + (8 * -3 + w * -3) 9 + -3w = 8w + (-24 + -3w) Reorder the terms: 9 + -3w = -24 + 8w + -3w Combine like terms: 8w + -3w = 5w 9 + -3w = -24 + 5w Solving 9 + -3w = -24 + 5w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5w' to each side of the equation. 9 + -3w + -5w = -24 + 5w + -5w Combine like terms: -3w + -5w = -8w 9 + -8w = -24 + 5w + -5w Combine like terms: 5w + -5w = 0 9 + -8w = -24 + 0 9 + -8w = -24 Add '-9' to each side of the equation. 9 + -9 + -8w = -24 + -9 Combine like terms: 9 + -9 = 0 0 + -8w = -24 + -9 -8w = -24 + -9 Combine like terms: -24 + -9 = -33 -8w = -33 Divide each side by '-8'. w = 4.125 Simplifying w = 4.125
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