



 
Hi James, Suppose $x = 5$ then the equation becomes \[10 = 2 + 10\] and you can add 10 to each side to get \[0 = 2.\] But this is clearly not true so $x \neq 10.$ This argument is valid no matter what value of $x$ you try. You can add $2x$ to each side of the equation to yield \[0 = 2.\] which is not true. Hence there is no number $x$ that satisfies \[2x = 2 + 2x.\] Penny  


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