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Simplifying 3(4w + -2) + 6(w + 4) + -3 = 4w + -7(w + 2) + 5(3w + 7) Reorder the terms: 3(-2 + 4w) + 6(w + 4) + -3 = 4w + -7(w + 2) + 5(3w + 7) (-2 * 3 + 4w * 3) + 6(w + 4) + -3 = 4w + -7(w + 2) + 5(3w + 7) (-6 + 12w) + 6(w + 4) + -3 = 4w + -7(w + 2) + 5(3w + 7) Reorder the terms: -6 + 12w + 6(4 + w) + -3 = 4w + -7(w + 2) + 5(3w + 7) -6 + 12w + (4 * 6 + w * 6) + -3 = 4w + -7(w + 2) + 5(3w + 7) -6 + 12w + (24 + 6w) + -3 = 4w + -7(w + 2) + 5(3w + 7) Reorder the terms: -6 + 24 + -3 + 12w + 6w = 4w + -7(w + 2) + 5(3w + 7) Combine like terms: -6 + 24 = 18 18 + -3 + 12w + 6w = 4w + -7(w + 2) + 5(3w + 7) Combine like terms: 18 + -3 = 15 15 + 12w + 6w = 4w + -7(w + 2) + 5(3w + 7) Combine like terms: 12w + 6w = 18w 15 + 18w = 4w + -7(w + 2) + 5(3w + 7) Reorder the terms: 15 + 18w = 4w + -7(2 + w) + 5(3w + 7) 15 + 18w = 4w + (2 * -7 + w * -7) + 5(3w + 7) 15 + 18w = 4w + (-14 + -7w) + 5(3w + 7) Reorder the terms: 15 + 18w = 4w + -14 + -7w + 5(7 + 3w) 15 + 18w = 4w + -14 + -7w + (7 * 5 + 3w * 5) 15 + 18w = 4w + -14 + -7w + (35 + 15w) Reorder the terms: 15 + 18w = -14 + 35 + 4w + -7w + 15w Combine like terms: -14 + 35 = 21 15 + 18w = 21 + 4w + -7w + 15w Combine like terms: 4w + -7w = -3w 15 + 18w = 21 + -3w + 15w Combine like terms: -3w + 15w = 12w 15 + 18w = 21 + 12w Solving 15 + 18w = 21 + 12w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12w' to each side of the equation. 15 + 18w + -12w = 21 + 12w + -12w Combine like terms: 18w + -12w = 6w 15 + 6w = 21 + 12w + -12w Combine like terms: 12w + -12w = 0 15 + 6w = 21 + 0 15 + 6w = 21 Add '-15' to each side of the equation. 15 + -15 + 6w = 21 + -15 Combine like terms: 15 + -15 = 0 0 + 6w = 21 + -15 6w = 21 + -15 Combine like terms: 21 + -15 = 6 6w = 6 Divide each side by '6'. w = 1 Simplifying w = 1
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