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