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Simplifying 8 + -1(3w + -2) = 5(w + -3) + -1(4w + -3) Reorder the terms: 8 + -1(-2 + 3w) = 5(w + -3) + -1(4w + -3) 8 + (-2 * -1 + 3w * -1) = 5(w + -3) + -1(4w + -3) 8 + (2 + -3w) = 5(w + -3) + -1(4w + -3) Combine like terms: 8 + 2 = 10 10 + -3w = 5(w + -3) + -1(4w + -3) Reorder the terms: 10 + -3w = 5(-3 + w) + -1(4w + -3) 10 + -3w = (-3 * 5 + w * 5) + -1(4w + -3) 10 + -3w = (-15 + 5w) + -1(4w + -3) Reorder the terms: 10 + -3w = -15 + 5w + -1(-3 + 4w) 10 + -3w = -15 + 5w + (-3 * -1 + 4w * -1) 10 + -3w = -15 + 5w + (3 + -4w) Reorder the terms: 10 + -3w = -15 + 3 + 5w + -4w Combine like terms: -15 + 3 = -12 10 + -3w = -12 + 5w + -4w Combine like terms: 5w + -4w = 1w 10 + -3w = -12 + 1w Solving 10 + -3w = -12 + 1w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1w' to each side of the equation. 10 + -3w + -1w = -12 + 1w + -1w Combine like terms: -3w + -1w = -4w 10 + -4w = -12 + 1w + -1w Combine like terms: 1w + -1w = 0 10 + -4w = -12 + 0 10 + -4w = -12 Add '-10' to each side of the equation. 10 + -10 + -4w = -12 + -10 Combine like terms: 10 + -10 = 0 0 + -4w = -12 + -10 -4w = -12 + -10 Combine like terms: -12 + -10 = -22 -4w = -22 Divide each side by '-4'. w = 5.5 Simplifying w = 5.5
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