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Simplifying 32 + -3(2w + 1) = 7w + -3(7 + w) Reorder the terms: 32 + -3(1 + 2w) = 7w + -3(7 + w) 32 + (1 * -3 + 2w * -3) = 7w + -3(7 + w) 32 + (-3 + -6w) = 7w + -3(7 + w) Combine like terms: 32 + -3 = 29 29 + -6w = 7w + -3(7 + w) 29 + -6w = 7w + (7 * -3 + w * -3) 29 + -6w = 7w + (-21 + -3w) Reorder the terms: 29 + -6w = -21 + 7w + -3w Combine like terms: 7w + -3w = 4w 29 + -6w = -21 + 4w Solving 29 + -6w = -21 + 4w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4w' to each side of the equation. 29 + -6w + -4w = -21 + 4w + -4w Combine like terms: -6w + -4w = -10w 29 + -10w = -21 + 4w + -4w Combine like terms: 4w + -4w = 0 29 + -10w = -21 + 0 29 + -10w = -21 Add '-29' to each side of the equation. 29 + -29 + -10w = -21 + -29 Combine like terms: 29 + -29 = 0 0 + -10w = -21 + -29 -10w = -21 + -29 Combine like terms: -21 + -29 = -50 -10w = -50 Divide each side by '-10'. w = 5 Simplifying w = 5
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