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Simplifying 11 + 4w = 3(-1w + 5) + 7(3w + 2) Reorder the terms: 11 + 4w = 3(5 + -1w) + 7(3w + 2) 11 + 4w = (5 * 3 + -1w * 3) + 7(3w + 2) 11 + 4w = (15 + -3w) + 7(3w + 2) Reorder the terms: 11 + 4w = 15 + -3w + 7(2 + 3w) 11 + 4w = 15 + -3w + (2 * 7 + 3w * 7) 11 + 4w = 15 + -3w + (14 + 21w) Reorder the terms: 11 + 4w = 15 + 14 + -3w + 21w Combine like terms: 15 + 14 = 29 11 + 4w = 29 + -3w + 21w Combine like terms: -3w + 21w = 18w 11 + 4w = 29 + 18w Solving 11 + 4w = 29 + 18w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-18w' to each side of the equation. 11 + 4w + -18w = 29 + 18w + -18w Combine like terms: 4w + -18w = -14w 11 + -14w = 29 + 18w + -18w Combine like terms: 18w + -18w = 0 11 + -14w = 29 + 0 11 + -14w = 29 Add '-11' to each side of the equation. 11 + -11 + -14w = 29 + -11 Combine like terms: 11 + -11 = 0 0 + -14w = 29 + -11 -14w = 29 + -11 Combine like terms: 29 + -11 = 18 -14w = 18 Divide each side by '-14'. w = -1.285714286 Simplifying w = -1.285714286
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