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.
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.
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?
How many solutions are there? How do you know? Can you prove it?
What happens to the inequality when the sign of the scale factor changes? Why?
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
Could any other value of x other than x = 7 satisfy your equation? Why or why not?
How many such equations can one construct [i.e., how many sets {a,b,c,d} are there]? How do you know?
What questions could/would you put to your students based on this applet?