Solving Equations with Variables on Both Sides

Identity- An equation that is true for every possible value of the variable.

-You can replace the variable with any value and the expressions on each side are equivalent.

Example: x+1=x+1

An equation has no solution if there is no value of the variable that makes the equation true.

Example- x+1=x+2

I can solve equations with variables on both sides to identify equations that are identities or have no solution.

How can you solve equations with variables on both sides?

You can use the properties of equality and inverse operations to write a series of simpler equivalent equations.

Steps:
-Write the original equation.
-Subtract 2x from each side. The coefficient 2 is less than the coefficient 5, so it is easier to subtract.
-Simplify. Now there is only one variable term. 
-Subtract 2 from each side.
-Simplify

Get the variable on one side of the equation and the numeric terms on the other side!

How do you know?