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Simplifying 4(w + -7) + -1(-9w + -1) = 12w Reorder the terms: 4(-7 + w) + -1(-9w + -1) = 12w (-7 * 4 + w * 4) + -1(-9w + -1) = 12w (-28 + 4w) + -1(-9w + -1) = 12w Reorder the terms: -28 + 4w + -1(-1 + -9w) = 12w -28 + 4w + (-1 * -1 + -9w * -1) = 12w -28 + 4w + (1 + 9w) = 12w Reorder the terms: -28 + 1 + 4w + 9w = 12w Combine like terms: -28 + 1 = -27 -27 + 4w + 9w = 12w Combine like terms: 4w + 9w = 13w -27 + 13w = 12w Solving -27 + 13w = 12w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12w' to each side of the equation. -27 + 13w + -12w = 12w + -12w Combine like terms: 13w + -12w = 1w -27 + 1w = 12w + -12w Combine like terms: 12w + -12w = 0 -27 + 1w = 0 Add '27' to each side of the equation. -27 + 27 + 1w = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 1w = 0 + 27 1w = 0 + 27 Combine like terms: 0 + 27 = 27 1w = 27 Divide each side by '1'. w = 27 Simplifying w = 27
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