SOLUTION: solve the equation. if it is an identity(all real numbers) or a contradiction ( no solution) so state. 2x-6+x=4x-6-x

Algebra ->  Equations -> SOLUTION: solve the equation. if it is an identity(all real numbers) or a contradiction ( no solution) so state. 2x-6+x=4x-6-x      Log On


   

Question 490756: solve the equation. if it is an identity(all real numbers) or a contradiction ( no solution) so state.
2x-6+x=4x-6-x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x-6%2Bx=4x-6-x Start with the given equation.


3x-6=4x-6-x Combine like terms on the left side.


3x-6=3x-6 Combine like terms on the right side.


3x=3x-6%2B6 Add 6 to both sides.


3x-3x=-6%2B6 Subtract 3x from both sides.


0x=-6%2B6 Combine like terms on the left side.


0x=0 Combine like terms on the right side.


0=0 Simplify.


Since this equation is ALWAYS true for any x value, this means x can equal any number.


So there are an infinite number of solutions.


This means that this equation is an identity.