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Simplifying (w + -3) + -5(w + 7) = (w + 3) + -1(7w + 5) Reorder the terms: (-3 + w) + -5(w + 7) = (w + 3) + -1(7w + 5) Remove parenthesis around (-3 + w) -3 + w + -5(w + 7) = (w + 3) + -1(7w + 5) Reorder the terms: -3 + w + -5(7 + w) = (w + 3) + -1(7w + 5) -3 + w + (7 * -5 + w * -5) = (w + 3) + -1(7w + 5) -3 + w + (-35 + -5w) = (w + 3) + -1(7w + 5) Reorder the terms: -3 + -35 + w + -5w = (w + 3) + -1(7w + 5) Combine like terms: -3 + -35 = -38 -38 + w + -5w = (w + 3) + -1(7w + 5) Combine like terms: w + -5w = -4w -38 + -4w = (w + 3) + -1(7w + 5) Reorder the terms: -38 + -4w = (3 + w) + -1(7w + 5) Remove parenthesis around (3 + w) -38 + -4w = 3 + w + -1(7w + 5) Reorder the terms: -38 + -4w = 3 + w + -1(5 + 7w) -38 + -4w = 3 + w + (5 * -1 + 7w * -1) -38 + -4w = 3 + w + (-5 + -7w) Reorder the terms: -38 + -4w = 3 + -5 + w + -7w Combine like terms: 3 + -5 = -2 -38 + -4w = -2 + w + -7w Combine like terms: w + -7w = -6w -38 + -4w = -2 + -6w Solving -38 + -4w = -2 + -6w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6w' to each side of the equation. -38 + -4w + 6w = -2 + -6w + 6w Combine like terms: -4w + 6w = 2w -38 + 2w = -2 + -6w + 6w Combine like terms: -6w + 6w = 0 -38 + 2w = -2 + 0 -38 + 2w = -2 Add '38' to each side of the equation. -38 + 38 + 2w = -2 + 38 Combine like terms: -38 + 38 = 0 0 + 2w = -2 + 38 2w = -2 + 38 Combine like terms: -2 + 38 = 36 2w = 36 Divide each side by '2'. w = 18 Simplifying w = 18
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