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Simplifying 3w + -1[4w + -2(w + -5)] + -1 = 2(3 + -1w) + -17 Reorder the terms: 3w + -1[4w + -2(-5 + w)] + -1 = 2(3 + -1w) + -17 3w + -1[4w + (-5 * -2 + w * -2)] + -1 = 2(3 + -1w) + -17 3w + -1[4w + (10 + -2w)] + -1 = 2(3 + -1w) + -17 Reorder the terms: 3w + -1[10 + 4w + -2w] + -1 = 2(3 + -1w) + -17 Combine like terms: 4w + -2w = 2w 3w + -1[10 + 2w] + -1 = 2(3 + -1w) + -17 3w + [10 * -1 + 2w * -1] + -1 = 2(3 + -1w) + -17 3w + [-10 + -2w] + -1 = 2(3 + -1w) + -17 Reorder the terms: -10 + -1 + 3w + -2w = 2(3 + -1w) + -17 Combine like terms: -10 + -1 = -11 -11 + 3w + -2w = 2(3 + -1w) + -17 Combine like terms: 3w + -2w = 1w -11 + 1w = 2(3 + -1w) + -17 -11 + 1w = (3 * 2 + -1w * 2) + -17 -11 + 1w = (6 + -2w) + -17 Reorder the terms: -11 + 1w = 6 + -17 + -2w Combine like terms: 6 + -17 = -11 -11 + 1w = -11 + -2w Add '11' to each side of the equation. -11 + 11 + 1w = -11 + 11 + -2w Combine like terms: -11 + 11 = 0 0 + 1w = -11 + 11 + -2w 1w = -11 + 11 + -2w Combine like terms: -11 + 11 = 0 1w = 0 + -2w 1w = -2w Solving 1w = -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. 1w + 2w = -2w + 2w Combine like terms: 1w + 2w = 3w 3w = -2w + 2w Combine like terms: -2w + 2w = 0 3w = 0 Divide each side by '3'. w = 0 Simplifying w = 0
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