The solution of a linear equation is a number - let's call it a. The solution of a linear inequality is a range of numbers, say all the numbers less than a, or all the numbers greater than a.[br][br]To UNsolve a linear equation or inequality, drag the GOLD dot in this panel to set the solution. The other panel will show you a linear equation or inequality that has that solution.[br][br]You can drag the dots in the right hand panel to see other equations or inequalities that have the same solution set. Each of the colored dots control one function - the WHITE dot controls both functions. Why is it permissible to change only one function in an equation or inequality that is a comparison of two functions? [br][br]How many solutions are there? How do you know? Can you prove it?[br]What happens to the inequality when the sign of the scale factor changes? Why?[br][br]Challenge - Make up an equation [i.e., find values for a, b, c, and d] of the form ax + b = cx + d with solution x = 7 and a, b, c, d <>0[br][br]Could any other value of x other than x = 7 satisfy your equation? Why or why not?[br][br]How many such equations can one construct [i.e., how many sets {a,b,c,d} are there]? How do you know?[br][br][color=#ff0000][i][b]What questions could/would you put to your students based on this applet?[/b][/i][/color]