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Simplifying 5(w + 1) + -7 = 2(w + -1) + 2w Reorder the terms: 5(1 + w) + -7 = 2(w + -1) + 2w (1 * 5 + w * 5) + -7 = 2(w + -1) + 2w (5 + 5w) + -7 = 2(w + -1) + 2w Reorder the terms: 5 + -7 + 5w = 2(w + -1) + 2w Combine like terms: 5 + -7 = -2 -2 + 5w = 2(w + -1) + 2w Reorder the terms: -2 + 5w = 2(-1 + w) + 2w -2 + 5w = (-1 * 2 + w * 2) + 2w -2 + 5w = (-2 + 2w) + 2w Combine like terms: 2w + 2w = 4w -2 + 5w = -2 + 4w Add '2' to each side of the equation. -2 + 2 + 5w = -2 + 2 + 4w Combine like terms: -2 + 2 = 0 0 + 5w = -2 + 2 + 4w 5w = -2 + 2 + 4w Combine like terms: -2 + 2 = 0 5w = 0 + 4w 5w = 4w Solving 5w = 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. 5w + -4w = 4w + -4w Combine like terms: 5w + -4w = 1w 1w = 4w + -4w Combine like terms: 4w + -4w = 0 1w = 0 Divide each side by '1'. w = 0 Simplifying w = 0
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