Whats wrong with this argument Suppose x and y represent two real numbers, where x 7 y

Chapter 4, Problem 89

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Whats wrong with this argument? Suppose x and y represent two real numbers, where x 7 y. 2 7 1 2(y - x) 7 1(y - x) 2y - 2x 7 y - x y - 2x 7 -x y 7 x This is a true statement. Multiply both sides by y - x. Use the distributive property. Subtract y from both sides. Add 2x to both sides. The final inequality, y 7 x, is impossible because we were initially given x 7 y.

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