SEARCH HOME
 Math Central Quandaries & Queries
 Question from james, a student: 2x = 2+2x can you help me find what x epauls?

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

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.