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Simplifying 3x + 2y + z = x + y + 5z Solving 3x + 2y + z = x + y + 5z Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 3x + 2y + -1x + z = x + y + -1x + 5z Reorder the terms: 3x + -1x + 2y + z = x + y + -1x + 5z Combine like terms: 3x + -1x = 2x 2x + 2y + z = x + y + -1x + 5z Reorder the terms: 2x + 2y + z = x + -1x + y + 5z Combine like terms: x + -1x = 0 2x + 2y + z = 0 + y + 5z 2x + 2y + z = y + 5z Add '-2y' to each side of the equation. 2x + 2y + -2y + z = y + -2y + 5z Combine like terms: 2y + -2y = 0 2x + 0 + z = y + -2y + 5z 2x + z = y + -2y + 5z Combine like terms: y + -2y = -1y 2x + z = -1y + 5z Add '-1z' to each side of the equation. 2x + z + -1z = -1y + 5z + -1z Combine like terms: z + -1z = 0 2x + 0 = -1y + 5z + -1z 2x = -1y + 5z + -1z Combine like terms: 5z + -1z = 4z 2x = -1y + 4z Divide each side by '2'. x = -0.5y + 2z Simplifying x = -0.5y + 2z
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