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Simplifying 2[w + -1(2w + 4) + 3] = 2w + 1 Reorder the terms: 2[w + -1(4 + 2w) + 3] = 2w + 1 2[w + (4 * -1 + 2w * -1) + 3] = 2w + 1 2[w + (-4 + -2w) + 3] = 2w + 1 Reorder the terms: 2[-4 + 3 + w + -2w] = 2w + 1 Combine like terms: -4 + 3 = -1 2[-1 + w + -2w] = 2w + 1 Combine like terms: w + -2w = -1w 2[-1 + -1w] = 2w + 1 [-1 * 2 + -1w * 2] = 2w + 1 [-2 + -2w] = 2w + 1 Reorder the terms: -2 + -2w = 1 + 2w Solving -2 + -2w = 1 + 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 = 1 + 2w + -2w Combine like terms: -2w + -2w = -4w -2 + -4w = 1 + 2w + -2w Combine like terms: 2w + -2w = 0 -2 + -4w = 1 + 0 -2 + -4w = 1 Add '2' to each side of the equation. -2 + 2 + -4w = 1 + 2 Combine like terms: -2 + 2 = 0 0 + -4w = 1 + 2 -4w = 1 + 2 Combine like terms: 1 + 2 = 3 -4w = 3 Divide each side by '-4'. w = -0.75 Simplifying w = -0.75
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