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Simplifying 3x + 5y + -3z + 7w = 82 Reorder the terms: 7w + 3x + 5y + -3z = 82 Solving 7w + 3x + 5y + -3z = 82 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3x' to each side of the equation. 7w + 3x + 5y + -3x + -3z = 82 + -3x Reorder the terms: 7w + 3x + -3x + 5y + -3z = 82 + -3x Combine like terms: 3x + -3x = 0 7w + 0 + 5y + -3z = 82 + -3x 7w + 5y + -3z = 82 + -3x Add '-5y' to each side of the equation. 7w + 5y + -5y + -3z = 82 + -3x + -5y Combine like terms: 5y + -5y = 0 7w + 0 + -3z = 82 + -3x + -5y 7w + -3z = 82 + -3x + -5y Add '3z' to each side of the equation. 7w + -3z + 3z = 82 + -3x + -5y + 3z Combine like terms: -3z + 3z = 0 7w + 0 = 82 + -3x + -5y + 3z 7w = 82 + -3x + -5y + 3z Divide each side by '7'. w = 11.71428571 + -0.4285714286x + -0.7142857143y + 0.4285714286z Simplifying w = 11.71428571 + -0.4285714286x + -0.7142857143y + 0.4285714286z
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