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