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Simplifying 2(w + 5) + 3(w + -1) = 8w + -4 + -2(w + 3) Reorder the terms: 2(5 + w) + 3(w + -1) = 8w + -4 + -2(w + 3) (5 * 2 + w * 2) + 3(w + -1) = 8w + -4 + -2(w + 3) (10 + 2w) + 3(w + -1) = 8w + -4 + -2(w + 3) Reorder the terms: 10 + 2w + 3(-1 + w) = 8w + -4 + -2(w + 3) 10 + 2w + (-1 * 3 + w * 3) = 8w + -4 + -2(w + 3) 10 + 2w + (-3 + 3w) = 8w + -4 + -2(w + 3) Reorder the terms: 10 + -3 + 2w + 3w = 8w + -4 + -2(w + 3) Combine like terms: 10 + -3 = 7 7 + 2w + 3w = 8w + -4 + -2(w + 3) Combine like terms: 2w + 3w = 5w 7 + 5w = 8w + -4 + -2(w + 3) Reorder the terms: 7 + 5w = 8w + -4 + -2(3 + w) 7 + 5w = 8w + -4 + (3 * -2 + w * -2) 7 + 5w = 8w + -4 + (-6 + -2w) Reorder the terms: 7 + 5w = -4 + -6 + 8w + -2w Combine like terms: -4 + -6 = -10 7 + 5w = -10 + 8w + -2w Combine like terms: 8w + -2w = 6w 7 + 5w = -10 + 6w Solving 7 + 5w = -10 + 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. 7 + 5w + -6w = -10 + 6w + -6w Combine like terms: 5w + -6w = -1w 7 + -1w = -10 + 6w + -6w Combine like terms: 6w + -6w = 0 7 + -1w = -10 + 0 7 + -1w = -10 Add '-7' to each side of the equation. 7 + -7 + -1w = -10 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = -10 + -7 -1w = -10 + -7 Combine like terms: -10 + -7 = -17 -1w = -17 Divide each side by '-1'. w = 17 Simplifying w = 17
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