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