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Simplifying 7(-1w + 5) + 3(5w + 2) = -1w + 3 + -3w Reorder the terms: 7(5 + -1w) + 3(5w + 2) = -1w + 3 + -3w (5 * 7 + -1w * 7) + 3(5w + 2) = -1w + 3 + -3w (35 + -7w) + 3(5w + 2) = -1w + 3 + -3w Reorder the terms: 35 + -7w + 3(2 + 5w) = -1w + 3 + -3w 35 + -7w + (2 * 3 + 5w * 3) = -1w + 3 + -3w 35 + -7w + (6 + 15w) = -1w + 3 + -3w Reorder the terms: 35 + 6 + -7w + 15w = -1w + 3 + -3w Combine like terms: 35 + 6 = 41 41 + -7w + 15w = -1w + 3 + -3w Combine like terms: -7w + 15w = 8w 41 + 8w = -1w + 3 + -3w Reorder the terms: 41 + 8w = 3 + -1w + -3w Combine like terms: -1w + -3w = -4w 41 + 8w = 3 + -4w Solving 41 + 8w = 3 + -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. 41 + 8w + 4w = 3 + -4w + 4w Combine like terms: 8w + 4w = 12w 41 + 12w = 3 + -4w + 4w Combine like terms: -4w + 4w = 0 41 + 12w = 3 + 0 41 + 12w = 3 Add '-41' to each side of the equation. 41 + -41 + 12w = 3 + -41 Combine like terms: 41 + -41 = 0 0 + 12w = 3 + -41 12w = 3 + -41 Combine like terms: 3 + -41 = -38 12w = -38 Divide each side by '12'. w = -3.166666667 Simplifying w = -3.166666667
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