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Simplifying 10 + -1(3w + -2) = -5(w + -3) + -1(4w + -3) Reorder the terms: 10 + -1(-2 + 3w) = -5(w + -3) + -1(4w + -3) 10 + (-2 * -1 + 3w * -1) = -5(w + -3) + -1(4w + -3) 10 + (2 + -3w) = -5(w + -3) + -1(4w + -3) Combine like terms: 10 + 2 = 12 12 + -3w = -5(w + -3) + -1(4w + -3) Reorder the terms: 12 + -3w = -5(-3 + w) + -1(4w + -3) 12 + -3w = (-3 * -5 + w * -5) + -1(4w + -3) 12 + -3w = (15 + -5w) + -1(4w + -3) Reorder the terms: 12 + -3w = 15 + -5w + -1(-3 + 4w) 12 + -3w = 15 + -5w + (-3 * -1 + 4w * -1) 12 + -3w = 15 + -5w + (3 + -4w) Reorder the terms: 12 + -3w = 15 + 3 + -5w + -4w Combine like terms: 15 + 3 = 18 12 + -3w = 18 + -5w + -4w Combine like terms: -5w + -4w = -9w 12 + -3w = 18 + -9w Solving 12 + -3w = 18 + -9w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9w' to each side of the equation. 12 + -3w + 9w = 18 + -9w + 9w Combine like terms: -3w + 9w = 6w 12 + 6w = 18 + -9w + 9w Combine like terms: -9w + 9w = 0 12 + 6w = 18 + 0 12 + 6w = 18 Add '-12' to each side of the equation. 12 + -12 + 6w = 18 + -12 Combine like terms: 12 + -12 = 0 0 + 6w = 18 + -12 6w = 18 + -12 Combine like terms: 18 + -12 = 6 6w = 6 Divide each side by '6'. w = 1 Simplifying w = 1
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