Expressions versus Equations

A difference between expressions and equations is what each represents.  An expression shows a math relationship.  One key to an expression is that there is no solution.  An expression does not have an answer. 

An expression, however, can be “evaluated.”  To evaluate an expression, substitute values for the variables.  The evaluation changes if you substitute different numbers in for the variables.  In this way, expressions can be simplified.  This is how we get numbers from expressions.

The expression 5x + 6 can be evaluated in many ways.  For instance:

      If x = 5, the value of the expression is 31. 

This is because 5 (5) + 6 = 25 + 6 = 31.

      If x = 12, the value of the expression is 66.

           This is because 5 (12) + 6 = 60 + 6 = 66.

      If x = -3, the value of the expression is –9.

            This is because 5 (-3) + 6 = -15 + 6 = -9.

An equation equates two expressions.  Equations, unlike expressions, can be solved.  For linear examples, there will be a single solution to an equation.  As the math abilities of the students progress, they will encounter equations that have more than one solution.

For example:  The equation 4y + 6 = 18 has one solution. 

                        Process to solve involves “isolating the variable”.

                                    4y + 6 = 18
                                          - 6     - 6
                                    4y       = 12

4                  4

 y       =    3

This means that only one value, 3, allows the two expressions have the same value.