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Simplifying 3x + 7y + 7z + 3w = 5x + 5y + 5z + 5w Reorder the terms: 3w + 3x + 7y + 7z = 5x + 5y + 5z + 5w Reorder the terms: 3w + 3x + 7y + 7z = 5w + 5x + 5y + 5z Solving 3w + 3x + 7y + 7z = 5w + 5x + 5y + 5z Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5w' to each side of the equation. 3w + 3x + 7y + -5w + 7z = 5w + 5x + 5y + -5w + 5z Reorder the terms: 3w + -5w + 3x + 7y + 7z = 5w + 5x + 5y + -5w + 5z Combine like terms: 3w + -5w = -2w -2w + 3x + 7y + 7z = 5w + 5x + 5y + -5w + 5z Reorder the terms: -2w + 3x + 7y + 7z = 5w + -5w + 5x + 5y + 5z Combine like terms: 5w + -5w = 0 -2w + 3x + 7y + 7z = 0 + 5x + 5y + 5z -2w + 3x + 7y + 7z = 5x + 5y + 5z Add '-3x' to each side of the equation. -2w + 3x + 7y + -3x + 7z = 5x + 5y + -3x + 5z Reorder the terms: -2w + 3x + -3x + 7y + 7z = 5x + 5y + -3x + 5z Combine like terms: 3x + -3x = 0 -2w + 0 + 7y + 7z = 5x + 5y + -3x + 5z -2w + 7y + 7z = 5x + 5y + -3x + 5z Reorder the terms: -2w + 7y + 7z = 5x + -3x + 5y + 5z Combine like terms: 5x + -3x = 2x -2w + 7y + 7z = 2x + 5y + 5z Add '-7y' to each side of the equation. -2w + 7y + -7y + 7z = 2x + 5y + -7y + 5z Combine like terms: 7y + -7y = 0 -2w + 0 + 7z = 2x + 5y + -7y + 5z -2w + 7z = 2x + 5y + -7y + 5z Combine like terms: 5y + -7y = -2y -2w + 7z = 2x + -2y + 5z Add '-7z' to each side of the equation. -2w + 7z + -7z = 2x + -2y + 5z + -7z Combine like terms: 7z + -7z = 0 -2w + 0 = 2x + -2y + 5z + -7z -2w = 2x + -2y + 5z + -7z Combine like terms: 5z + -7z = -2z -2w = 2x + -2y + -2z Divide each side by '-2'. w = -1x + y + z Simplifying w = -1x + y + z
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