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Simplifying (2w + -5) + -1(8 + -3w) = 4w + 17 + -1w Reorder the terms: (-5 + 2w) + -1(8 + -3w) = 4w + 17 + -1w Remove parenthesis around (-5 + 2w) -5 + 2w + -1(8 + -3w) = 4w + 17 + -1w -5 + 2w + (8 * -1 + -3w * -1) = 4w + 17 + -1w -5 + 2w + (-8 + 3w) = 4w + 17 + -1w Reorder the terms: -5 + -8 + 2w + 3w = 4w + 17 + -1w Combine like terms: -5 + -8 = -13 -13 + 2w + 3w = 4w + 17 + -1w Combine like terms: 2w + 3w = 5w -13 + 5w = 4w + 17 + -1w Reorder the terms: -13 + 5w = 17 + 4w + -1w Combine like terms: 4w + -1w = 3w -13 + 5w = 17 + 3w Solving -13 + 5w = 17 + 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. -13 + 5w + -3w = 17 + 3w + -3w Combine like terms: 5w + -3w = 2w -13 + 2w = 17 + 3w + -3w Combine like terms: 3w + -3w = 0 -13 + 2w = 17 + 0 -13 + 2w = 17 Add '13' to each side of the equation. -13 + 13 + 2w = 17 + 13 Combine like terms: -13 + 13 = 0 0 + 2w = 17 + 13 2w = 17 + 13 Combine like terms: 17 + 13 = 30 2w = 30 Divide each side by '2'. w = 15 Simplifying w = 15
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