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Simplifying -2(w + -7) + -1(1 + -1w) = 2(1 + w) + w + -3 Reorder the terms: -2(-7 + w) + -1(1 + -1w) = 2(1 + w) + w + -3 (-7 * -2 + w * -2) + -1(1 + -1w) = 2(1 + w) + w + -3 (14 + -2w) + -1(1 + -1w) = 2(1 + w) + w + -3 14 + -2w + (1 * -1 + -1w * -1) = 2(1 + w) + w + -3 14 + -2w + (-1 + 1w) = 2(1 + w) + w + -3 Reorder the terms: 14 + -1 + -2w + 1w = 2(1 + w) + w + -3 Combine like terms: 14 + -1 = 13 13 + -2w + 1w = 2(1 + w) + w + -3 Combine like terms: -2w + 1w = -1w 13 + -1w = 2(1 + w) + w + -3 13 + -1w = (1 * 2 + w * 2) + w + -3 13 + -1w = (2 + 2w) + w + -3 Reorder the terms: 13 + -1w = 2 + -3 + 2w + w Combine like terms: 2 + -3 = -1 13 + -1w = -1 + 2w + w Combine like terms: 2w + w = 3w 13 + -1w = -1 + 3w Solving 13 + -1w = -1 + 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 + -1w + -3w = -1 + 3w + -3w Combine like terms: -1w + -3w = -4w 13 + -4w = -1 + 3w + -3w Combine like terms: 3w + -3w = 0 13 + -4w = -1 + 0 13 + -4w = -1 Add '-13' to each side of the equation. 13 + -13 + -4w = -1 + -13 Combine like terms: 13 + -13 = 0 0 + -4w = -1 + -13 -4w = -1 + -13 Combine like terms: -1 + -13 = -14 -4w = -14 Divide each side by '-4'. w = 3.5 Simplifying w = 3.5
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