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Simplifying 9(w + -5) + -1(-4w + -2) = 12w Reorder the terms: 9(-5 + w) + -1(-4w + -2) = 12w (-5 * 9 + w * 9) + -1(-4w + -2) = 12w (-45 + 9w) + -1(-4w + -2) = 12w Reorder the terms: -45 + 9w + -1(-2 + -4w) = 12w -45 + 9w + (-2 * -1 + -4w * -1) = 12w -45 + 9w + (2 + 4w) = 12w Reorder the terms: -45 + 2 + 9w + 4w = 12w Combine like terms: -45 + 2 = -43 -43 + 9w + 4w = 12w Combine like terms: 9w + 4w = 13w -43 + 13w = 12w Solving -43 + 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. -43 + 13w + -12w = 12w + -12w Combine like terms: 13w + -12w = 1w -43 + 1w = 12w + -12w Combine like terms: 12w + -12w = 0 -43 + 1w = 0 Add '43' to each side of the equation. -43 + 43 + 1w = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 1w = 0 + 43 1w = 0 + 43 Combine like terms: 0 + 43 = 43 1w = 43 Divide each side by '1'. w = 43 Simplifying w = 43
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