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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 + 12w + 5 + -30w + -2(-8 + w) = 6(7w + -4) + 4w 8 + 12w + 5 + -30w + (-8 * -2 + w * -2) = 6(7w + -4) + 4w 8 + 12w + 5 + -30w + (16 + -2w) = 6(7w + -4) + 4w Reorder the terms: 8 + 5 + 16 + 12w + -30w + -2w = 6(7w + -4) + 4w Combine like terms: 8 + 5 = 13 13 + 16 + 12w + -30w + -2w = 6(7w + -4) + 4w Combine like terms: 13 + 16 = 29 29 + 12w + -30w + -2w = 6(7w + -4) + 4w Combine like terms: 12w + -30w = -18w 29 + -18w + -2w = 6(7w + -4) + 4w Combine like terms: -18w + -2w = -20w 29 + -20w = 6(7w + -4) + 4w Reorder the terms: 29 + -20w = 6(-4 + 7w) + 4w 29 + -20w = (-4 * 6 + 7w * 6) + 4w 29 + -20w = (-24 + 42w) + 4w Combine like terms: 42w + 4w = 46w 29 + -20w = -24 + 46w Solving 29 + -20w = -24 + 46w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-46w' to each side of the equation. 29 + -20w + -46w = -24 + 46w + -46w Combine like terms: -20w + -46w = -66w 29 + -66w = -24 + 46w + -46w Combine like terms: 46w + -46w = 0 29 + -66w = -24 + 0 29 + -66w = -24 Add '-29' to each side of the equation. 29 + -29 + -66w = -24 + -29 Combine like terms: 29 + -29 = 0 0 + -66w = -24 + -29 -66w = -24 + -29 Combine like terms: -24 + -29 = -53 -66w = -53 Divide each side by '-66'. w = 0.803030303 Simplifying w = 0.803030303
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