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Simplifying 6w + -1[5w + -3(w + -4)] + 1 = 2(1 + -1w) + 5 Reorder the terms: 6w + -1[5w + -3(-4 + w)] + 1 = 2(1 + -1w) + 5 6w + -1[5w + (-4 * -3 + w * -3)] + 1 = 2(1 + -1w) + 5 6w + -1[5w + (12 + -3w)] + 1 = 2(1 + -1w) + 5 Reorder the terms: 6w + -1[12 + 5w + -3w] + 1 = 2(1 + -1w) + 5 Combine like terms: 5w + -3w = 2w 6w + -1[12 + 2w] + 1 = 2(1 + -1w) + 5 6w + [12 * -1 + 2w * -1] + 1 = 2(1 + -1w) + 5 6w + [-12 + -2w] + 1 = 2(1 + -1w) + 5 Reorder the terms: -12 + 1 + 6w + -2w = 2(1 + -1w) + 5 Combine like terms: -12 + 1 = -11 -11 + 6w + -2w = 2(1 + -1w) + 5 Combine like terms: 6w + -2w = 4w -11 + 4w = 2(1 + -1w) + 5 -11 + 4w = (1 * 2 + -1w * 2) + 5 -11 + 4w = (2 + -2w) + 5 Reorder the terms: -11 + 4w = 2 + 5 + -2w Combine like terms: 2 + 5 = 7 -11 + 4w = 7 + -2w Solving -11 + 4w = 7 + -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. -11 + 4w + 2w = 7 + -2w + 2w Combine like terms: 4w + 2w = 6w -11 + 6w = 7 + -2w + 2w Combine like terms: -2w + 2w = 0 -11 + 6w = 7 + 0 -11 + 6w = 7 Add '11' to each side of the equation. -11 + 11 + 6w = 7 + 11 Combine like terms: -11 + 11 = 0 0 + 6w = 7 + 11 6w = 7 + 11 Combine like terms: 7 + 11 = 18 6w = 18 Divide each side by '6'. w = 3 Simplifying w = 3
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