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Simplifying 34 + -4(2w + 1) = 10w + -4(10 + w) Reorder the terms: 34 + -4(1 + 2w) = 10w + -4(10 + w) 34 + (1 * -4 + 2w * -4) = 10w + -4(10 + w) 34 + (-4 + -8w) = 10w + -4(10 + w) Combine like terms: 34 + -4 = 30 30 + -8w = 10w + -4(10 + w) 30 + -8w = 10w + (10 * -4 + w * -4) 30 + -8w = 10w + (-40 + -4w) Reorder the terms: 30 + -8w = -40 + 10w + -4w Combine like terms: 10w + -4w = 6w 30 + -8w = -40 + 6w Solving 30 + -8w = -40 + 6w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6w' to each side of the equation. 30 + -8w + -6w = -40 + 6w + -6w Combine like terms: -8w + -6w = -14w 30 + -14w = -40 + 6w + -6w Combine like terms: 6w + -6w = 0 30 + -14w = -40 + 0 30 + -14w = -40 Add '-30' to each side of the equation. 30 + -30 + -14w = -40 + -30 Combine like terms: 30 + -30 = 0 0 + -14w = -40 + -30 -14w = -40 + -30 Combine like terms: -40 + -30 = -70 -14w = -70 Divide each side by '-14'. w = 5 Simplifying w = 5
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