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Simplifying 5w + -7 + 7(w + -3) + -4(w + -9) = 0 Reorder the terms: 5w + -7 + 7(-3 + w) + -4(w + -9) = 0 5w + -7 + (-3 * 7 + w * 7) + -4(w + -9) = 0 5w + -7 + (-21 + 7w) + -4(w + -9) = 0 Reorder the terms: 5w + -7 + -21 + 7w + -4(-9 + w) = 0 5w + -7 + -21 + 7w + (-9 * -4 + w * -4) = 0 5w + -7 + -21 + 7w + (36 + -4w) = 0 Reorder the terms: -7 + -21 + 36 + 5w + 7w + -4w = 0 Combine like terms: -7 + -21 = -28 -28 + 36 + 5w + 7w + -4w = 0 Combine like terms: -28 + 36 = 8 8 + 5w + 7w + -4w = 0 Combine like terms: 5w + 7w = 12w 8 + 12w + -4w = 0 Combine like terms: 12w + -4w = 8w 8 + 8w = 0 Solving 8 + 8w = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 8w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 8w = 0 + -8 8w = 0 + -8 Combine like terms: 0 + -8 = -8 8w = -8 Divide each side by '8'. w = -1 Simplifying w = -1
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