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Simplifying 3x + 4y + 5z = 4x + 7y + 6z Solving 3x + 4y + 5z = 4x + 7y + 6z Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 3x + 4y + -4x + 5z = 4x + 7y + -4x + 6z Reorder the terms: 3x + -4x + 4y + 5z = 4x + 7y + -4x + 6z Combine like terms: 3x + -4x = -1x -1x + 4y + 5z = 4x + 7y + -4x + 6z Reorder the terms: -1x + 4y + 5z = 4x + -4x + 7y + 6z Combine like terms: 4x + -4x = 0 -1x + 4y + 5z = 0 + 7y + 6z -1x + 4y + 5z = 7y + 6z Add '-4y' to each side of the equation. -1x + 4y + -4y + 5z = 7y + -4y + 6z Combine like terms: 4y + -4y = 0 -1x + 0 + 5z = 7y + -4y + 6z -1x + 5z = 7y + -4y + 6z Combine like terms: 7y + -4y = 3y -1x + 5z = 3y + 6z Add '-5z' to each side of the equation. -1x + 5z + -5z = 3y + 6z + -5z Combine like terms: 5z + -5z = 0 -1x + 0 = 3y + 6z + -5z -1x = 3y + 6z + -5z Combine like terms: 6z + -5z = 1z -1x = 3y + 1z Divide each side by '-1'. x = -3y + -1z Simplifying x = -3y + -1z
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