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Simplifying -2w + -3w + -1(11 + -2w + 10w + -2) + -1(2 + -1w + -1w) = 4(-2w + 6 + -2w + -3) Reorder the terms: -2w + -3w + -1(11 + -2 + -2w + 10w) + -1(2 + -1w + -1w) = 4(-2w + 6 + -2w + -3) Combine like terms: 11 + -2 = 9 -2w + -3w + -1(9 + -2w + 10w) + -1(2 + -1w + -1w) = 4(-2w + 6 + -2w + -3) Combine like terms: -2w + 10w = 8w -2w + -3w + -1(9 + 8w) + -1(2 + -1w + -1w) = 4(-2w + 6 + -2w + -3) -2w + -3w + (9 * -1 + 8w * -1) + -1(2 + -1w + -1w) = 4(-2w + 6 + -2w + -3) -2w + -3w + (-9 + -8w) + -1(2 + -1w + -1w) = 4(-2w + 6 + -2w + -3) Combine like terms: -1w + -1w = -2w -2w + -3w + -9 + -8w + -1(2 + -2w) = 4(-2w + 6 + -2w + -3) -2w + -3w + -9 + -8w + (2 * -1 + -2w * -1) = 4(-2w + 6 + -2w + -3) -2w + -3w + -9 + -8w + (-2 + 2w) = 4(-2w + 6 + -2w + -3) Reorder the terms: -9 + -2 + -2w + -3w + -8w + 2w = 4(-2w + 6 + -2w + -3) Combine like terms: -9 + -2 = -11 -11 + -2w + -3w + -8w + 2w = 4(-2w + 6 + -2w + -3) Combine like terms: -2w + -3w = -5w -11 + -5w + -8w + 2w = 4(-2w + 6 + -2w + -3) Combine like terms: -5w + -8w = -13w -11 + -13w + 2w = 4(-2w + 6 + -2w + -3) Combine like terms: -13w + 2w = -11w -11 + -11w = 4(-2w + 6 + -2w + -3) Reorder the terms: -11 + -11w = 4(6 + -3 + -2w + -2w) Combine like terms: 6 + -3 = 3 -11 + -11w = 4(3 + -2w + -2w) Combine like terms: -2w + -2w = -4w -11 + -11w = 4(3 + -4w) -11 + -11w = (3 * 4 + -4w * 4) -11 + -11w = (12 + -16w) Solving -11 + -11w = 12 + -16w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '16w' to each side of the equation. -11 + -11w + 16w = 12 + -16w + 16w Combine like terms: -11w + 16w = 5w -11 + 5w = 12 + -16w + 16w Combine like terms: -16w + 16w = 0 -11 + 5w = 12 + 0 -11 + 5w = 12 Add '11' to each side of the equation. -11 + 11 + 5w = 12 + 11 Combine like terms: -11 + 11 = 0 0 + 5w = 12 + 11 5w = 12 + 11 Combine like terms: 12 + 11 = 23 5w = 23 Divide each side by '5'. w = 4.6 Simplifying w = 4.6
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