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Simplifying 6x + 3y + 0.1z = x + y + z Solving 6x + 3y + 0.1z = x + y + z 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. 6x + 3y + -1x + 0.1z = x + y + -1x + z Reorder the terms: 6x + -1x + 3y + 0.1z = x + y + -1x + z Combine like terms: 6x + -1x = 5x 5x + 3y + 0.1z = x + y + -1x + z Reorder the terms: 5x + 3y + 0.1z = x + -1x + y + z Combine like terms: x + -1x = 0 5x + 3y + 0.1z = 0 + y + z 5x + 3y + 0.1z = y + z Add '-3y' to each side of the equation. 5x + 3y + -3y + 0.1z = y + -3y + z Combine like terms: 3y + -3y = 0 5x + 0 + 0.1z = y + -3y + z 5x + 0.1z = y + -3y + z Combine like terms: y + -3y = -2y 5x + 0.1z = -2y + z Add '-0.1z' to each side of the equation. 5x + 0.1z + -0.1z = -2y + z + -0.1z Combine like terms: 0.1z + -0.1z = 0.0 5x + 0.0 = -2y + z + -0.1z 5x = -2y + z + -0.1z Combine like terms: z + -0.1z = 0.9z 5x = -2y + 0.9z Divide each side by '5'. x = -0.4y + 0.18z Simplifying x = -0.4y + 0.18z
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