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Simplifying 2[w + -1(4w + 7) + 1] = 2w + 12 Reorder the terms: 2[w + -1(7 + 4w) + 1] = 2w + 12 2[w + (7 * -1 + 4w * -1) + 1] = 2w + 12 2[w + (-7 + -4w) + 1] = 2w + 12 Reorder the terms: 2[-7 + 1 + w + -4w] = 2w + 12 Combine like terms: -7 + 1 = -6 2[-6 + w + -4w] = 2w + 12 Combine like terms: w + -4w = -3w 2[-6 + -3w] = 2w + 12 [-6 * 2 + -3w * 2] = 2w + 12 [-12 + -6w] = 2w + 12 Reorder the terms: -12 + -6w = 12 + 2w Solving -12 + -6w = 12 + 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. -12 + -6w + -2w = 12 + 2w + -2w Combine like terms: -6w + -2w = -8w -12 + -8w = 12 + 2w + -2w Combine like terms: 2w + -2w = 0 -12 + -8w = 12 + 0 -12 + -8w = 12 Add '12' to each side of the equation. -12 + 12 + -8w = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -8w = 12 + 12 -8w = 12 + 12 Combine like terms: 12 + 12 = 24 -8w = 24 Divide each side by '-8'. w = -3 Simplifying w = -3
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