Solving Equations with Variables

In the previous subset, you learned about mathematical expressions and how to solve mathematical expressions with variables.  In such a case, the variable could take on any value because the expression was not equated to anything.  However, this is not the case with equations with variables.  Because there are now two mathematical expressions being equated to each other, the variable, usually “x”, can’t just take on any value.  The variable x must be solved for by isolating it in the equation.  For example: 

7x + 5 = 5x – 3 

Here, two mathematical expressions involving variables are equated.  How do we go about solving for x?  First, let us group together what’s called “like terms”, i.e. terms that are the same (numbers by themselves called “constants”, variables of the same power, etc.).  Solving for x, therefore, can be performed: 

7x + 5 = 5x – 3 

7x – 5x + 5 + 3 = 0 or 7x -5x = -3 – 5 

2x + 8 = 0 (skip this step if in the above step you do it the right way) 

2x = -8 

x = -4  

As seen above, when solving mathematical equations involving variables, the variable can only hold specific values that satisfy the equation.