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Simplifying 4[5(w + 3) + -1(w + 1)] = 7(3 + w) Reorder the terms: 4[5(3 + w) + -1(w + 1)] = 7(3 + w) 4[(3 * 5 + w * 5) + -1(w + 1)] = 7(3 + w) 4[(15 + 5w) + -1(w + 1)] = 7(3 + w) Reorder the terms: 4[15 + 5w + -1(1 + w)] = 7(3 + w) 4[15 + 5w + (1 * -1 + w * -1)] = 7(3 + w) 4[15 + 5w + (-1 + -1w)] = 7(3 + w) Reorder the terms: 4[15 + -1 + 5w + -1w] = 7(3 + w) Combine like terms: 15 + -1 = 14 4[14 + 5w + -1w] = 7(3 + w) Combine like terms: 5w + -1w = 4w 4[14 + 4w] = 7(3 + w) [14 * 4 + 4w * 4] = 7(3 + w) [56 + 16w] = 7(3 + w) 56 + 16w = (3 * 7 + w * 7) 56 + 16w = (21 + 7w) Solving 56 + 16w = 21 + 7w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7w' to each side of the equation. 56 + 16w + -7w = 21 + 7w + -7w Combine like terms: 16w + -7w = 9w 56 + 9w = 21 + 7w + -7w Combine like terms: 7w + -7w = 0 56 + 9w = 21 + 0 56 + 9w = 21 Add '-56' to each side of the equation. 56 + -56 + 9w = 21 + -56 Combine like terms: 56 + -56 = 0 0 + 9w = 21 + -56 9w = 21 + -56 Combine like terms: 21 + -56 = -35 9w = -35 Divide each side by '9'. w = -3.888888889 Simplifying w = -3.888888889
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