Solve the equation 4x-14=4-2x. We expect most of you still remember how to do this and end up with x=3. How did you find the solution? You probably moved -2x to the left side of the equation (reversing the sign) and -14 to the right side. Then you added and subtracted where possible to generate 6x=18. From there you divided each side by 6 and arrived at the answer - x=3. Now here is a different question - What does x=3 symbolize? What have you found when you solve the equation 4x-14=4-2x? We expect that many can solve the problem we have provided, but have no idea what the solution represents.

You may not understand what you have found when you solved the problem you were presented because you were able to arrive at an answer by relying upon some well learned rules. Collectively, these rules represent an algorithm - a procedure that will generate a correct solution if followed correctly. The math standards encourage that students learn to solve equations in different ways because of the problem we have just attempted to demonstrate - rote algorithmic procedures do not assure understanding (National Council of Teachers of Mathematics, 1989). A spreadsheet provides one alternative to the algorithmic approach you have learned to rely on.

Look carefully at Figure 5.6. In row 3, you see a sequence of numerical values - 1, 2,3 etc. These numbers will be used as values for the variable x. The cell entries in row 4 are calculated by substituting the value for x from row 3 in the expression 4x-14. Using the spreadsheet, cell C4 would be assigned to the value =4*c3-14. Once entered, this formula could be copied to the other cells of row 4 to quickly generate the remaining values. Cell c5 would be calculated as =4-(2*c3). Again, the formula would be copied to the cells of row five.

A spreadsheet (this happens to be Microsoft Excel) usually allows the generation of graphs as an alternative way to represent data. If rows 4 and 5 are transformed into a line graph, the display contained in Figure 5.x is generated. If you look carefully, you should have a better understanding of what the solution to 4x-14=4-2x represents. It is the x value at the intersection of the lines defined by 4x-14 and 4-2x.

Figure 5.6: Spreadsheet Used to Solve Algebra Equation

Based on an article by Niess (1998).