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