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Simplifying 12 + -3(2w + 1) = 10w + -3(10 + w) Reorder the terms: 12 + -3(1 + 2w) = 10w + -3(10 + w) 12 + (1 * -3 + 2w * -3) = 10w + -3(10 + w) 12 + (-3 + -6w) = 10w + -3(10 + w) Combine like terms: 12 + -3 = 9 9 + -6w = 10w + -3(10 + w) 9 + -6w = 10w + (10 * -3 + w * -3) 9 + -6w = 10w + (-30 + -3w) Reorder the terms: 9 + -6w = -30 + 10w + -3w Combine like terms: 10w + -3w = 7w 9 + -6w = -30 + 7w Solving 9 + -6w = -30 + 7w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7w' to each side of the equation. 9 + -6w + -7w = -30 + 7w + -7w Combine like terms: -6w + -7w = -13w 9 + -13w = -30 + 7w + -7w Combine like terms: 7w + -7w = 0 9 + -13w = -30 + 0 9 + -13w = -30 Add '-9' to each side of the equation. 9 + -9 + -13w = -30 + -9 Combine like terms: 9 + -9 = 0 0 + -13w = -30 + -9 -13w = -30 + -9 Combine like terms: -30 + -9 = -39 -13w = -39 Divide each side by '-13'. w = 3 Simplifying w = 3
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