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Simplifying 34 + -2(2w + 1) = 12w + -2(12 + w) Reorder the terms: 34 + -2(1 + 2w) = 12w + -2(12 + w) 34 + (1 * -2 + 2w * -2) = 12w + -2(12 + w) 34 + (-2 + -4w) = 12w + -2(12 + w) Combine like terms: 34 + -2 = 32 32 + -4w = 12w + -2(12 + w) 32 + -4w = 12w + (12 * -2 + w * -2) 32 + -4w = 12w + (-24 + -2w) Reorder the terms: 32 + -4w = -24 + 12w + -2w Combine like terms: 12w + -2w = 10w 32 + -4w = -24 + 10w Solving 32 + -4w = -24 + 10w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10w' to each side of the equation. 32 + -4w + -10w = -24 + 10w + -10w Combine like terms: -4w + -10w = -14w 32 + -14w = -24 + 10w + -10w Combine like terms: 10w + -10w = 0 32 + -14w = -24 + 0 32 + -14w = -24 Add '-32' to each side of the equation. 32 + -32 + -14w = -24 + -32 Combine like terms: 32 + -32 = 0 0 + -14w = -24 + -32 -14w = -24 + -32 Combine like terms: -24 + -32 = -56 -14w = -56 Divide each side by '-14'. w = 4 Simplifying w = 4
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