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Simplifying 7(3w + -4) + 14(1 + -4w) = 8(2 + -5w) Reorder the terms: 7(-4 + 3w) + 14(1 + -4w) = 8(2 + -5w) (-4 * 7 + 3w * 7) + 14(1 + -4w) = 8(2 + -5w) (-28 + 21w) + 14(1 + -4w) = 8(2 + -5w) -28 + 21w + (1 * 14 + -4w * 14) = 8(2 + -5w) -28 + 21w + (14 + -56w) = 8(2 + -5w) Reorder the terms: -28 + 14 + 21w + -56w = 8(2 + -5w) Combine like terms: -28 + 14 = -14 -14 + 21w + -56w = 8(2 + -5w) Combine like terms: 21w + -56w = -35w -14 + -35w = 8(2 + -5w) -14 + -35w = (2 * 8 + -5w * 8) -14 + -35w = (16 + -40w) Solving -14 + -35w = 16 + -40w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '40w' to each side of the equation. -14 + -35w + 40w = 16 + -40w + 40w Combine like terms: -35w + 40w = 5w -14 + 5w = 16 + -40w + 40w Combine like terms: -40w + 40w = 0 -14 + 5w = 16 + 0 -14 + 5w = 16 Add '14' to each side of the equation. -14 + 14 + 5w = 16 + 14 Combine like terms: -14 + 14 = 0 0 + 5w = 16 + 14 5w = 16 + 14 Combine like terms: 16 + 14 = 30 5w = 30 Divide each side by '5'. w = 6 Simplifying w = 6
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