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Simplifying 7(w + -1) + 5 = 3 + -1(4 + w) Reorder the terms: 7(-1 + w) + 5 = 3 + -1(4 + w) (-1 * 7 + w * 7) + 5 = 3 + -1(4 + w) (-7 + 7w) + 5 = 3 + -1(4 + w) Reorder the terms: -7 + 5 + 7w = 3 + -1(4 + w) Combine like terms: -7 + 5 = -2 -2 + 7w = 3 + -1(4 + w) -2 + 7w = 3 + (4 * -1 + w * -1) -2 + 7w = 3 + (-4 + -1w) Combine like terms: 3 + -4 = -1 -2 + 7w = -1 + -1w Solving -2 + 7w = -1 + -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 + 7w + w = -1 + -1w + w Combine like terms: 7w + w = 8w -2 + 8w = -1 + -1w + w Combine like terms: -1w + w = 0 -2 + 8w = -1 + 0 -2 + 8w = -1 Add '2' to each side of the equation. -2 + 2 + 8w = -1 + 2 Combine like terms: -2 + 2 = 0 0 + 8w = -1 + 2 8w = -1 + 2 Combine like terms: -1 + 2 = 1 8w = 1 Divide each side by '8'. w = 0.125 Simplifying w = 0.125
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