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Simplifying 7(w + 1) = 5(2w + -2) + 1 Reorder the terms: 7(1 + w) = 5(2w + -2) + 1 (1 * 7 + w * 7) = 5(2w + -2) + 1 (7 + 7w) = 5(2w + -2) + 1 Reorder the terms: 7 + 7w = 5(-2 + 2w) + 1 7 + 7w = (-2 * 5 + 2w * 5) + 1 7 + 7w = (-10 + 10w) + 1 Reorder the terms: 7 + 7w = -10 + 1 + 10w Combine like terms: -10 + 1 = -9 7 + 7w = -9 + 10w Solving 7 + 7w = -9 + 10w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10w' to each side of the equation. 7 + 7w + -10w = -9 + 10w + -10w Combine like terms: 7w + -10w = -3w 7 + -3w = -9 + 10w + -10w Combine like terms: 10w + -10w = 0 7 + -3w = -9 + 0 7 + -3w = -9 Add '-7' to each side of the equation. 7 + -7 + -3w = -9 + -7 Combine like terms: 7 + -7 = 0 0 + -3w = -9 + -7 -3w = -9 + -7 Combine like terms: -9 + -7 = -16 -3w = -16 Divide each side by '-3'. w = 5.333333333 Simplifying w = 5.333333333
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