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Simplifying 12 + -3(2w + 1) = 7w + -3(7 + -1w) Reorder the terms: 12 + -3(1 + 2w) = 7w + -3(7 + -1w) 12 + (1 * -3 + 2w * -3) = 7w + -3(7 + -1w) 12 + (-3 + -6w) = 7w + -3(7 + -1w) Combine like terms: 12 + -3 = 9 9 + -6w = 7w + -3(7 + -1w) 9 + -6w = 7w + (7 * -3 + -1w * -3) 9 + -6w = 7w + (-21 + 3w) Reorder the terms: 9 + -6w = -21 + 7w + 3w Combine like terms: 7w + 3w = 10w 9 + -6w = -21 + 10w Solving 9 + -6w = -21 + 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. 9 + -6w + -10w = -21 + 10w + -10w Combine like terms: -6w + -10w = -16w 9 + -16w = -21 + 10w + -10w Combine like terms: 10w + -10w = 0 9 + -16w = -21 + 0 9 + -16w = -21 Add '-9' to each side of the equation. 9 + -9 + -16w = -21 + -9 Combine like terms: 9 + -9 = 0 0 + -16w = -21 + -9 -16w = -21 + -9 Combine like terms: -21 + -9 = -30 -16w = -30 Divide each side by '-16'. w = 1.875 Simplifying w = 1.875
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