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Simplifying 4(3w + -9) + 51 = -3(w + 15) Reorder the terms: 4(-9 + 3w) + 51 = -3(w + 15) (-9 * 4 + 3w * 4) + 51 = -3(w + 15) (-36 + 12w) + 51 = -3(w + 15) Reorder the terms: -36 + 51 + 12w = -3(w + 15) Combine like terms: -36 + 51 = 15 15 + 12w = -3(w + 15) Reorder the terms: 15 + 12w = -3(15 + w) 15 + 12w = (15 * -3 + w * -3) 15 + 12w = (-45 + -3w) Solving 15 + 12w = -45 + -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. 15 + 12w + 3w = -45 + -3w + 3w Combine like terms: 12w + 3w = 15w 15 + 15w = -45 + -3w + 3w Combine like terms: -3w + 3w = 0 15 + 15w = -45 + 0 15 + 15w = -45 Add '-15' to each side of the equation. 15 + -15 + 15w = -45 + -15 Combine like terms: 15 + -15 = 0 0 + 15w = -45 + -15 15w = -45 + -15 Combine like terms: -45 + -15 = -60 15w = -60 Divide each side by '15'. w = -4 Simplifying w = -4
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