In mathematics, we work with equivalent equations all the time. Think about the process for solving a multistep equation. We might start with something such as 5x + 3 = 23 Using inverse operations, we create a series of equivalent equations in order to find a value for x.




An equivalent equation  

An equivalent equation 
The equations above are all considered equivalent equations, because they have the same solution. In each equation, the solution is x = 4.
In order to determine if two equations are equivalent, we will solve each equation, and then compare their solutions. If their solutions are the same, we can say the equations are equivalent. If the solutions are not the same, we know that the equations are not equivalent.
Determine if the equations below are equivalent:





Solve each equation separately:



Subtract 6  Subtract 9  
Divide by  Multiply by 2 
The solutions to our equations are x = 2 and x = –2. Since the solutions are not the same, the two equations are not equivalent.