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