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Simplifying 12 + -3(2w + 1) = 5w + -3(5 + w) Reorder the terms: 12 + -3(1 + 2w) = 5w + -3(5 + w) 12 + (1 * -3 + 2w * -3) = 5w + -3(5 + w) 12 + (-3 + -6w) = 5w + -3(5 + w) Combine like terms: 12 + -3 = 9 9 + -6w = 5w + -3(5 + w) 9 + -6w = 5w + (5 * -3 + w * -3) 9 + -6w = 5w + (-15 + -3w) Reorder the terms: 9 + -6w = -15 + 5w + -3w Combine like terms: 5w + -3w = 2w 9 + -6w = -15 + 2w Solving 9 + -6w = -15 + 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 + -6w + -2w = -15 + 2w + -2w Combine like terms: -6w + -2w = -8w 9 + -8w = -15 + 2w + -2w Combine like terms: 2w + -2w = 0 9 + -8w = -15 + 0 9 + -8w = -15 Add '-9' to each side of the equation. 9 + -9 + -8w = -15 + -9 Combine like terms: 9 + -9 = 0 0 + -8w = -15 + -9 -8w = -15 + -9 Combine like terms: -15 + -9 = -24 -8w = -24 Divide each side by '-8'. w = 3 Simplifying w = 3
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