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Simplifying 8 + -1(3w + -2) = -5(w + -2) + -1(4w + -3) Reorder the terms: 8 + -1(-2 + 3w) = -5(w + -2) + -1(4w + -3) 8 + (-2 * -1 + 3w * -1) = -5(w + -2) + -1(4w + -3) 8 + (2 + -3w) = -5(w + -2) + -1(4w + -3) Combine like terms: 8 + 2 = 10 10 + -3w = -5(w + -2) + -1(4w + -3) Reorder the terms: 10 + -3w = -5(-2 + w) + -1(4w + -3) 10 + -3w = (-2 * -5 + w * -5) + -1(4w + -3) 10 + -3w = (10 + -5w) + -1(4w + -3) Reorder the terms: 10 + -3w = 10 + -5w + -1(-3 + 4w) 10 + -3w = 10 + -5w + (-3 * -1 + 4w * -1) 10 + -3w = 10 + -5w + (3 + -4w) Reorder the terms: 10 + -3w = 10 + 3 + -5w + -4w Combine like terms: 10 + 3 = 13 10 + -3w = 13 + -5w + -4w Combine like terms: -5w + -4w = -9w 10 + -3w = 13 + -9w Solving 10 + -3w = 13 + -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. 10 + -3w + 9w = 13 + -9w + 9w Combine like terms: -3w + 9w = 6w 10 + 6w = 13 + -9w + 9w Combine like terms: -9w + 9w = 0 10 + 6w = 13 + 0 10 + 6w = 13 Add '-10' to each side of the equation. 10 + -10 + 6w = 13 + -10 Combine like terms: 10 + -10 = 0 0 + 6w = 13 + -10 6w = 13 + -10 Combine like terms: 13 + -10 = 3 6w = 3 Divide each side by '6'. w = 0.5 Simplifying w = 0.5
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