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Simplifying 3x + -7y + -1z + 4w = 1 Reorder the terms: 4w + 3x + -7y + -1z = 1 Solving 4w + 3x + -7y + -1z = 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 + -7y + -3x + -1z = 1 + -3x Reorder the terms: 4w + 3x + -3x + -7y + -1z = 1 + -3x Combine like terms: 3x + -3x = 0 4w + 0 + -7y + -1z = 1 + -3x 4w + -7y + -1z = 1 + -3x Add '7y' to each side of the equation. 4w + -7y + 7y + -1z = 1 + -3x + 7y Combine like terms: -7y + 7y = 0 4w + 0 + -1z = 1 + -3x + 7y 4w + -1z = 1 + -3x + 7y Add 'z' to each side of the equation. 4w + -1z + z = 1 + -3x + 7y + z Combine like terms: -1z + z = 0 4w + 0 = 1 + -3x + 7y + z 4w = 1 + -3x + 7y + z Divide each side by '4'. w = 0.25 + -0.75x + 1.75y + 0.25z Simplifying w = 0.25 + -0.75x + 1.75y + 0.25z
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