Simplifying versus Solving

Simplifying and solving are similar.  The difference between them is an extension of the difference between expressions and equations.  Simplifying can be done with either expressions or equations. 

Simplifying involves making the math sentence shorter.  Simplifying also makes math sentences easier to interpret and understand.  Simplifying involves combining terms with the same variable and combining numbers.  This can be done with expressions or equations.

For example:

      4y + 9 – 2 – 3y becomes y + 7. 

              This is because 4y – 3y is the same as y and 9 – 2 is the same as 7.

      9x + 8 – 12 + 12x = 2p + 9p – 8 becomes 
21x – 4 = 11p – 8.

                  Reordering the equation:

                              9x + 12x + 8 – 12 = 2p + 9p – 8

                                   21x         - 4     =    11p – 8

Solving is only done with equations.  Solving involves finding the value or values that makes the equation, or math sentence, true.

For example:

      The value t = 4 makes the two sides of the equation 5t + 4 = 8t – 8 the same value.

                        5t + 4 = 8t – 8
           -5t         -5t       
                    4 = 3t – 8
                  +8        + 8

                              12 = 3t 
                    3     3

                                 4 = t