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Simplifying 3w + 4w + -1 = 12 + 3(w + 1) Reorder the terms: -1 + 3w + 4w = 12 + 3(w + 1) Combine like terms: 3w + 4w = 7w -1 + 7w = 12 + 3(w + 1) Reorder the terms: -1 + 7w = 12 + 3(1 + w) -1 + 7w = 12 + (1 * 3 + w * 3) -1 + 7w = 12 + (3 + 3w) Combine like terms: 12 + 3 = 15 -1 + 7w = 15 + 3w Solving -1 + 7w = 15 + 3w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3w' to each side of the equation. -1 + 7w + -3w = 15 + 3w + -3w Combine like terms: 7w + -3w = 4w -1 + 4w = 15 + 3w + -3w Combine like terms: 3w + -3w = 0 -1 + 4w = 15 + 0 -1 + 4w = 15 Add '1' to each side of the equation. -1 + 1 + 4w = 15 + 1 Combine like terms: -1 + 1 = 0 0 + 4w = 15 + 1 4w = 15 + 1 Combine like terms: 15 + 1 = 16 4w = 16 Divide each side by '4'. w = 4 Simplifying w = 4
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