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Simplifying 5w + -1(3w + -4) + 4 = 14 + -1(w + 1) Reorder the terms: 5w + -1(-4 + 3w) + 4 = 14 + -1(w + 1) 5w + (-4 * -1 + 3w * -1) + 4 = 14 + -1(w + 1) 5w + (4 + -3w) + 4 = 14 + -1(w + 1) Reorder the terms: 4 + 4 + 5w + -3w = 14 + -1(w + 1) Combine like terms: 4 + 4 = 8 8 + 5w + -3w = 14 + -1(w + 1) Combine like terms: 5w + -3w = 2w 8 + 2w = 14 + -1(w + 1) Reorder the terms: 8 + 2w = 14 + -1(1 + w) 8 + 2w = 14 + (1 * -1 + w * -1) 8 + 2w = 14 + (-1 + -1w) Combine like terms: 14 + -1 = 13 8 + 2w = 13 + -1w Solving 8 + 2w = 13 + -1w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add 'w' to each side of the equation. 8 + 2w + w = 13 + -1w + w Combine like terms: 2w + w = 3w 8 + 3w = 13 + -1w + w Combine like terms: -1w + w = 0 8 + 3w = 13 + 0 8 + 3w = 13 Add '-8' to each side of the equation. 8 + -8 + 3w = 13 + -8 Combine like terms: 8 + -8 = 0 0 + 3w = 13 + -8 3w = 13 + -8 Combine like terms: 13 + -8 = 5 3w = 5 Divide each side by '3'. w = 1.666666667 Simplifying w = 1.666666667
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