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Simplifying 2[w + -1(2w + 13) + 40] = 2(w + 3) Reorder the terms: 2[w + -1(13 + 2w) + 40] = 2(w + 3) 2[w + (13 * -1 + 2w * -1) + 40] = 2(w + 3) 2[w + (-13 + -2w) + 40] = 2(w + 3) Reorder the terms: 2[-13 + 40 + w + -2w] = 2(w + 3) Combine like terms: -13 + 40 = 27 2[27 + w + -2w] = 2(w + 3) Combine like terms: w + -2w = -1w 2[27 + -1w] = 2(w + 3) [27 * 2 + -1w * 2] = 2(w + 3) [54 + -2w] = 2(w + 3) Reorder the terms: 54 + -2w = 2(3 + w) 54 + -2w = (3 * 2 + w * 2) 54 + -2w = (6 + 2w) Solving 54 + -2w = 6 + 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. 54 + -2w + -2w = 6 + 2w + -2w Combine like terms: -2w + -2w = -4w 54 + -4w = 6 + 2w + -2w Combine like terms: 2w + -2w = 0 54 + -4w = 6 + 0 54 + -4w = 6 Add '-54' to each side of the equation. 54 + -54 + -4w = 6 + -54 Combine like terms: 54 + -54 = 0 0 + -4w = 6 + -54 -4w = 6 + -54 Combine like terms: 6 + -54 = -48 -4w = -48 Divide each side by '-4'. w = 12 Simplifying w = 12
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