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Simplifying x + 2y + -3z + 4w = 12 Reorder the terms: 4w + x + 2y + -3z = 12 Solving 4w + x + 2y + -3z = 12 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1x' to each side of the equation. 4w + x + 2y + -1x + -3z = 12 + -1x Reorder the terms: 4w + x + -1x + 2y + -3z = 12 + -1x Combine like terms: x + -1x = 0 4w + 0 + 2y + -3z = 12 + -1x 4w + 2y + -3z = 12 + -1x Add '-2y' to each side of the equation. 4w + 2y + -2y + -3z = 12 + -1x + -2y Combine like terms: 2y + -2y = 0 4w + 0 + -3z = 12 + -1x + -2y 4w + -3z = 12 + -1x + -2y Add '3z' to each side of the equation. 4w + -3z + 3z = 12 + -1x + -2y + 3z Combine like terms: -3z + 3z = 0 4w + 0 = 12 + -1x + -2y + 3z 4w = 12 + -1x + -2y + 3z Divide each side by '4'. w = 3 + -0.25x + -0.5y + 0.75z Simplifying w = 3 + -0.25x + -0.5y + 0.75z
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