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Simplifying 6w + -1(4w + -7) = 5w + -1(4 + -9w) + (4w + 35) Reorder the terms: 6w + -1(-7 + 4w) = 5w + -1(4 + -9w) + (4w + 35) 6w + (-7 * -1 + 4w * -1) = 5w + -1(4 + -9w) + (4w + 35) 6w + (7 + -4w) = 5w + -1(4 + -9w) + (4w + 35) Reorder the terms: 7 + 6w + -4w = 5w + -1(4 + -9w) + (4w + 35) Combine like terms: 6w + -4w = 2w 7 + 2w = 5w + -1(4 + -9w) + (4w + 35) 7 + 2w = 5w + (4 * -1 + -9w * -1) + (4w + 35) 7 + 2w = 5w + (-4 + 9w) + (4w + 35) Reorder the terms: 7 + 2w = 5w + -4 + 9w + (35 + 4w) Remove parenthesis around (35 + 4w) 7 + 2w = 5w + -4 + 9w + 35 + 4w Reorder the terms: 7 + 2w = -4 + 35 + 5w + 9w + 4w Combine like terms: -4 + 35 = 31 7 + 2w = 31 + 5w + 9w + 4w Combine like terms: 5w + 9w = 14w 7 + 2w = 31 + 14w + 4w Combine like terms: 14w + 4w = 18w 7 + 2w = 31 + 18w Solving 7 + 2w = 31 + 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. 7 + 2w + -18w = 31 + 18w + -18w Combine like terms: 2w + -18w = -16w 7 + -16w = 31 + 18w + -18w Combine like terms: 18w + -18w = 0 7 + -16w = 31 + 0 7 + -16w = 31 Add '-7' to each side of the equation. 7 + -7 + -16w = 31 + -7 Combine like terms: 7 + -7 = 0 0 + -16w = 31 + -7 -16w = 31 + -7 Combine like terms: 31 + -7 = 24 -16w = 24 Divide each side by '-16'. w = -1.5 Simplifying w = -1.5
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