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Simplifying 4(3w + 2) + -5(6w + -1) = 2(w + -8) + -6(7w + -4) + 4w Reorder the terms: 4(2 + 3w) + -5(6w + -1) = 2(w + -8) + -6(7w + -4) + 4w (2 * 4 + 3w * 4) + -5(6w + -1) = 2(w + -8) + -6(7w + -4) + 4w (8 + 12w) + -5(6w + -1) = 2(w + -8) + -6(7w + -4) + 4w Reorder the terms: 8 + 12w + -5(-1 + 6w) = 2(w + -8) + -6(7w + -4) + 4w 8 + 12w + (-1 * -5 + 6w * -5) = 2(w + -8) + -6(7w + -4) + 4w 8 + 12w + (5 + -30w) = 2(w + -8) + -6(7w + -4) + 4w Reorder the terms: 8 + 5 + 12w + -30w = 2(w + -8) + -6(7w + -4) + 4w Combine like terms: 8 + 5 = 13 13 + 12w + -30w = 2(w + -8) + -6(7w + -4) + 4w Combine like terms: 12w + -30w = -18w 13 + -18w = 2(w + -8) + -6(7w + -4) + 4w Reorder the terms: 13 + -18w = 2(-8 + w) + -6(7w + -4) + 4w 13 + -18w = (-8 * 2 + w * 2) + -6(7w + -4) + 4w 13 + -18w = (-16 + 2w) + -6(7w + -4) + 4w Reorder the terms: 13 + -18w = -16 + 2w + -6(-4 + 7w) + 4w 13 + -18w = -16 + 2w + (-4 * -6 + 7w * -6) + 4w 13 + -18w = -16 + 2w + (24 + -42w) + 4w Reorder the terms: 13 + -18w = -16 + 24 + 2w + -42w + 4w Combine like terms: -16 + 24 = 8 13 + -18w = 8 + 2w + -42w + 4w Combine like terms: 2w + -42w = -40w 13 + -18w = 8 + -40w + 4w Combine like terms: -40w + 4w = -36w 13 + -18w = 8 + -36w Solving 13 + -18w = 8 + -36w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '36w' to each side of the equation. 13 + -18w + 36w = 8 + -36w + 36w Combine like terms: -18w + 36w = 18w 13 + 18w = 8 + -36w + 36w Combine like terms: -36w + 36w = 0 13 + 18w = 8 + 0 13 + 18w = 8 Add '-13' to each side of the equation. 13 + -13 + 18w = 8 + -13 Combine like terms: 13 + -13 = 0 0 + 18w = 8 + -13 18w = 8 + -13 Combine like terms: 8 + -13 = -5 18w = -5 Divide each side by '18'. w = -0.2777777778 Simplifying w = -0.2777777778
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