# Linear Inequalities solved w/ graphs & symbols

- Author:
- Judah L Schwartz

- Topic:
- Function Graph, Inequalities

A linear inequality is always of the form . For example, in the inequality we can regard as and as
Solving a linear inequality means transforming the original inequality into a new inequality that has the function on one side of the equal sign and a number (which is a constant function) on the other side.
In this case the 'solution equation' is (why is 1.5 a function?)
The app allows you to enter a linear function f(x) = mx + b by varying m and b sliders and
a function g(x) = Mx + B by varying M and B sliders.
.
Why does the applet behave as it does if m = M?
Why does it behave as it does when m=M and b=B ?

**The fundamental question this applet poses is FOR WHAT VALUES OF x IS THE**You may solve your inequality*GREEN*FUNCTION LARGER THAN THE*BLUE*FUNCTION?__by dragging the__**graphically***,***GREEN***and***BLUE***dots on the graph in order to produce a 'solution inequality' of the form***WHITE***- Dragging the***Challenge***dot changes both functions, but dragging the***WHITE***dot changes only the***GREEN***function, and dragging the***GREEN***dot changes only the***BLUE***function. This means that when you drag either the GREEN dot or the BLUE dot you are changing only***BLUE****side of the inequality!! - Why is this legitimate? - Why are we taught that you must do the same thing to both sides of an inequality? - What is true about all the legitimate things you can do to a linear inequality? - What are the symbolic operations that correspond to dragging each of the dots? You may also solve your inequality***ONE*__by using sliders to change the linear and constant terms on each side of the inequality. - What are the graphical operations that correspond to each of the sliders? Particular attention should be paid to the behavior of the SCALE slider.__**symbolically****What other questions could/would you pose to your students based on this applet ?**