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Simplifying 7(3w + 4w + -1w + 0wx) + 1 = -83 Anything times zero is zero. 7(3w + 4w + -1w + 0wx) + 1 = -83 Reorder the terms: 7(0 + 3w + 4w + -1w) + 1 = -83 Remove the zero: 7(3w + 4w + -1w) + 1 = -83 Combine like terms: 3w + 4w = 7w 7(7w + -1w) + 1 = -83 Combine like terms: 7w + -1w = 6w 7(6w) + 1 = -83 Remove parenthesis around (6w) 7 * 6w + 1 = -83 Multiply 7 * 6 42w + 1 = -83 Reorder the terms: 1 + 42w = -83 Solving 1 + 42w = -83 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 42w = -83 + -1 Combine like terms: 1 + -1 = 0 0 + 42w = -83 + -1 42w = -83 + -1 Combine like terms: -83 + -1 = -84 42w = -84 Divide each side by '42'. w = -2 Simplifying w = -2
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