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