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Simplifying 5w + -1(3w + -4) + 4 = 14 + -2(w + 1) Reorder the terms: 5w + -1(-4 + 3w) + 4 = 14 + -2(w + 1) 5w + (-4 * -1 + 3w * -1) + 4 = 14 + -2(w + 1) 5w + (4 + -3w) + 4 = 14 + -2(w + 1) Reorder the terms: 4 + 4 + 5w + -3w = 14 + -2(w + 1) Combine like terms: 4 + 4 = 8 8 + 5w + -3w = 14 + -2(w + 1) Combine like terms: 5w + -3w = 2w 8 + 2w = 14 + -2(w + 1) Reorder the terms: 8 + 2w = 14 + -2(1 + w) 8 + 2w = 14 + (1 * -2 + w * -2) 8 + 2w = 14 + (-2 + -2w) Combine like terms: 14 + -2 = 12 8 + 2w = 12 + -2w Solving 8 + 2w = 12 + -2w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2w' to each side of the equation. 8 + 2w + 2w = 12 + -2w + 2w Combine like terms: 2w + 2w = 4w 8 + 4w = 12 + -2w + 2w Combine like terms: -2w + 2w = 0 8 + 4w = 12 + 0 8 + 4w = 12 Add '-8' to each side of the equation. 8 + -8 + 4w = 12 + -8 Combine like terms: 8 + -8 = 0 0 + 4w = 12 + -8 4w = 12 + -8 Combine like terms: 12 + -8 = 4 4w = 4 Divide each side by '4'. w = 1 Simplifying w = 1
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