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Simplifying 3x + -1y + 2z + 4w = 1 Reorder the terms: 4w + 3x + -1y + 2z = 1 Solving 4w + 3x + -1y + 2z = 1 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. 4w + 3x + -1y + -3x + 2z = 1 + -3x Reorder the terms: 4w + 3x + -3x + -1y + 2z = 1 + -3x Combine like terms: 3x + -3x = 0 4w + 0 + -1y + 2z = 1 + -3x 4w + -1y + 2z = 1 + -3x Add 'y' to each side of the equation. 4w + -1y + y + 2z = 1 + -3x + y Combine like terms: -1y + y = 0 4w + 0 + 2z = 1 + -3x + y 4w + 2z = 1 + -3x + y Add '-2z' to each side of the equation. 4w + 2z + -2z = 1 + -3x + y + -2z Combine like terms: 2z + -2z = 0 4w + 0 = 1 + -3x + y + -2z 4w = 1 + -3x + y + -2z Divide each side by '4'. w = 0.25 + -0.75x + 0.25y + -0.5z Simplifying w = 0.25 + -0.75x + 0.25y + -0.5z
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