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Simplifying 5(1 + -2w) + 8(w + 3) = 77 (1 * 5 + -2w * 5) + 8(w + 3) = 77 (5 + -10w) + 8(w + 3) = 77 Reorder the terms: 5 + -10w + 8(3 + w) = 77 5 + -10w + (3 * 8 + w * 8) = 77 5 + -10w + (24 + 8w) = 77 Reorder the terms: 5 + 24 + -10w + 8w = 77 Combine like terms: 5 + 24 = 29 29 + -10w + 8w = 77 Combine like terms: -10w + 8w = -2w 29 + -2w = 77 Solving 29 + -2w = 77 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -2w = 77 + -29 Combine like terms: 29 + -29 = 0 0 + -2w = 77 + -29 -2w = 77 + -29 Combine like terms: 77 + -29 = 48 -2w = 48 Divide each side by '-2'. w = -24 Simplifying w = -24
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