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Simplifying 5(w + 8) + -1(-3w + -7) = 7w Reorder the terms: 5(8 + w) + -1(-3w + -7) = 7w (8 * 5 + w * 5) + -1(-3w + -7) = 7w (40 + 5w) + -1(-3w + -7) = 7w Reorder the terms: 40 + 5w + -1(-7 + -3w) = 7w 40 + 5w + (-7 * -1 + -3w * -1) = 7w 40 + 5w + (7 + 3w) = 7w Reorder the terms: 40 + 7 + 5w + 3w = 7w Combine like terms: 40 + 7 = 47 47 + 5w + 3w = 7w Combine like terms: 5w + 3w = 8w 47 + 8w = 7w Solving 47 + 8w = 7w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7w' to each side of the equation. 47 + 8w + -7w = 7w + -7w Combine like terms: 8w + -7w = 1w 47 + 1w = 7w + -7w Combine like terms: 7w + -7w = 0 47 + 1w = 0 Add '-47' to each side of the equation. 47 + -47 + 1w = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 1w = 0 + -47 1w = 0 + -47 Combine like terms: 0 + -47 = -47 1w = -47 Divide each side by '1'. w = -47 Simplifying w = -47
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