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Simplifying 3[4(w + 2) + -1(w + 1)] = 5(2 + w) Reorder the terms: 3[4(2 + w) + -1(w + 1)] = 5(2 + w) 3[(2 * 4 + w * 4) + -1(w + 1)] = 5(2 + w) 3[(8 + 4w) + -1(w + 1)] = 5(2 + w) Reorder the terms: 3[8 + 4w + -1(1 + w)] = 5(2 + w) 3[8 + 4w + (1 * -1 + w * -1)] = 5(2 + w) 3[8 + 4w + (-1 + -1w)] = 5(2 + w) Reorder the terms: 3[8 + -1 + 4w + -1w] = 5(2 + w) Combine like terms: 8 + -1 = 7 3[7 + 4w + -1w] = 5(2 + w) Combine like terms: 4w + -1w = 3w 3[7 + 3w] = 5(2 + w) [7 * 3 + 3w * 3] = 5(2 + w) [21 + 9w] = 5(2 + w) 21 + 9w = (2 * 5 + w * 5) 21 + 9w = (10 + 5w) Solving 21 + 9w = 10 + 5w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5w' to each side of the equation. 21 + 9w + -5w = 10 + 5w + -5w Combine like terms: 9w + -5w = 4w 21 + 4w = 10 + 5w + -5w Combine like terms: 5w + -5w = 0 21 + 4w = 10 + 0 21 + 4w = 10 Add '-21' to each side of the equation. 21 + -21 + 4w = 10 + -21 Combine like terms: 21 + -21 = 0 0 + 4w = 10 + -21 4w = 10 + -21 Combine like terms: 10 + -21 = -11 4w = -11 Divide each side by '4'. w = -2.75 Simplifying w = -2.75
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