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Simplifying -5(8 + -1w) + 3w + 10 = -12 + 7w + 3(4 + -4w) (8 * -5 + -1w * -5) + 3w + 10 = -12 + 7w + 3(4 + -4w) (-40 + 5w) + 3w + 10 = -12 + 7w + 3(4 + -4w) Reorder the terms: -40 + 10 + 5w + 3w = -12 + 7w + 3(4 + -4w) Combine like terms: -40 + 10 = -30 -30 + 5w + 3w = -12 + 7w + 3(4 + -4w) Combine like terms: 5w + 3w = 8w -30 + 8w = -12 + 7w + 3(4 + -4w) -30 + 8w = -12 + 7w + (4 * 3 + -4w * 3) -30 + 8w = -12 + 7w + (12 + -12w) Reorder the terms: -30 + 8w = -12 + 12 + 7w + -12w Combine like terms: -12 + 12 = 0 -30 + 8w = 0 + 7w + -12w -30 + 8w = 7w + -12w Combine like terms: 7w + -12w = -5w -30 + 8w = -5w Solving -30 + 8w = -5w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5w' to each side of the equation. -30 + 8w + 5w = -5w + 5w Combine like terms: 8w + 5w = 13w -30 + 13w = -5w + 5w Combine like terms: -5w + 5w = 0 -30 + 13w = 0 Add '30' to each side of the equation. -30 + 30 + 13w = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 13w = 0 + 30 13w = 0 + 30 Combine like terms: 0 + 30 = 30 13w = 30 Divide each side by '13'. w = 2.307692308 Simplifying w = 2.307692308
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