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Simplifying 6w + 2(w + -1) = 14 + -1(w + 1) Reorder the terms: 6w + 2(-1 + w) = 14 + -1(w + 1) 6w + (-1 * 2 + w * 2) = 14 + -1(w + 1) 6w + (-2 + 2w) = 14 + -1(w + 1) Reorder the terms: -2 + 6w + 2w = 14 + -1(w + 1) Combine like terms: 6w + 2w = 8w -2 + 8w = 14 + -1(w + 1) Reorder the terms: -2 + 8w = 14 + -1(1 + w) -2 + 8w = 14 + (1 * -1 + w * -1) -2 + 8w = 14 + (-1 + -1w) Combine like terms: 14 + -1 = 13 -2 + 8w = 13 + -1w Solving -2 + 8w = 13 + -1w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add 'w' to each side of the equation. -2 + 8w + w = 13 + -1w + w Combine like terms: 8w + w = 9w -2 + 9w = 13 + -1w + w Combine like terms: -1w + w = 0 -2 + 9w = 13 + 0 -2 + 9w = 13 Add '2' to each side of the equation. -2 + 2 + 9w = 13 + 2 Combine like terms: -2 + 2 = 0 0 + 9w = 13 + 2 9w = 13 + 2 Combine like terms: 13 + 2 = 15 9w = 15 Divide each side by '9'. w = 1.666666667 Simplifying w = 1.666666667
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