Back to Unit 6

Balancing and Solving Equations

An equation must always remain in balance.

 In order to do this while solving you must use opposite operations.

Operation

Opposite Operation

Addition

Subtraction

Subtraction

Addition

Multiplication

Division

Division

Multiplication

 

You will work in steps.  Begin with addition and subtraction (unless the whole expression is multiplied or divided).  Then multiplication and division.  Then exponents (the opposite is the root). 

 The object is to get the variable alone on one side of the equal sign.   

Here is an example of solving for x in a simple equation:  2x + 4 = 14 

 Use the opposite operation on both sides of the equal to get rid of the unwanted expression.

                                                                  

                                                         - 4     -4 

                                                             

Text Box: Now we want the x alone on one side of the equal, so we divide by 2 (the opposite of multiplying by 2) to both sides of the equation.

 
Text Box: Step 2:
                                                2x      = 10

                                                Text Box: Our solution is x=5.  Now we check the answer by substituting the 5 into the original equation.
                                                

 

  

            Check:  

                           

                               

 

Next Page - More examples