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Simplifying 3(12w + -10) = 8(2w + -6) + 6(3w + 5) Reorder the terms: 3(-10 + 12w) = 8(2w + -6) + 6(3w + 5) (-10 * 3 + 12w * 3) = 8(2w + -6) + 6(3w + 5) (-30 + 36w) = 8(2w + -6) + 6(3w + 5) Reorder the terms: -30 + 36w = 8(-6 + 2w) + 6(3w + 5) -30 + 36w = (-6 * 8 + 2w * 8) + 6(3w + 5) -30 + 36w = (-48 + 16w) + 6(3w + 5) Reorder the terms: -30 + 36w = -48 + 16w + 6(5 + 3w) -30 + 36w = -48 + 16w + (5 * 6 + 3w * 6) -30 + 36w = -48 + 16w + (30 + 18w) Reorder the terms: -30 + 36w = -48 + 30 + 16w + 18w Combine like terms: -48 + 30 = -18 -30 + 36w = -18 + 16w + 18w Combine like terms: 16w + 18w = 34w -30 + 36w = -18 + 34w Solving -30 + 36w = -18 + 34w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-34w' to each side of the equation. -30 + 36w + -34w = -18 + 34w + -34w Combine like terms: 36w + -34w = 2w -30 + 2w = -18 + 34w + -34w Combine like terms: 34w + -34w = 0 -30 + 2w = -18 + 0 -30 + 2w = -18 Add '30' to each side of the equation. -30 + 30 + 2w = -18 + 30 Combine like terms: -30 + 30 = 0 0 + 2w = -18 + 30 2w = -18 + 30 Combine like terms: -18 + 30 = 12 2w = 12 Divide each side by '2'. w = 6 Simplifying w = 6
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