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Simplifying 5(3w + 4) + 32w = 8(3w + 21) + -7(3w + 4) Reorder the terms: 5(4 + 3w) + 32w = 8(3w + 21) + -7(3w + 4) (4 * 5 + 3w * 5) + 32w = 8(3w + 21) + -7(3w + 4) (20 + 15w) + 32w = 8(3w + 21) + -7(3w + 4) Combine like terms: 15w + 32w = 47w 20 + 47w = 8(3w + 21) + -7(3w + 4) Reorder the terms: 20 + 47w = 8(21 + 3w) + -7(3w + 4) 20 + 47w = (21 * 8 + 3w * 8) + -7(3w + 4) 20 + 47w = (168 + 24w) + -7(3w + 4) Reorder the terms: 20 + 47w = 168 + 24w + -7(4 + 3w) 20 + 47w = 168 + 24w + (4 * -7 + 3w * -7) 20 + 47w = 168 + 24w + (-28 + -21w) Reorder the terms: 20 + 47w = 168 + -28 + 24w + -21w Combine like terms: 168 + -28 = 140 20 + 47w = 140 + 24w + -21w Combine like terms: 24w + -21w = 3w 20 + 47w = 140 + 3w Solving 20 + 47w = 140 + 3w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3w' to each side of the equation. 20 + 47w + -3w = 140 + 3w + -3w Combine like terms: 47w + -3w = 44w 20 + 44w = 140 + 3w + -3w Combine like terms: 3w + -3w = 0 20 + 44w = 140 + 0 20 + 44w = 140 Add '-20' to each side of the equation. 20 + -20 + 44w = 140 + -20 Combine like terms: 20 + -20 = 0 0 + 44w = 140 + -20 44w = 140 + -20 Combine like terms: 140 + -20 = 120 44w = 120 Divide each side by '44'. w = 2.727272727 Simplifying w = 2.727272727
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