Inequalities

Understanding the INEQUALITY

 Graphing an Open Sentence

that is an INEQUALITY.

For example:

Graph the Solution Set for   "5 <  x"

Some students are taught to always have the

" the >  or < will NOT ALWAYS point in the

direction of the shaded solution. 

SINCE  "5 < x" is EQUIVALENT TO "x > 5"

the graph is  ...

READ the inequality starting with "X".

"5 < x"

would be read "X is GREATER than 5."

Since we are graphing "X's", this method

of translation will lead to the correct

direction of the ARROW in the graph.

*******************************

You may want to get a larger view of a VIDEO.
Click on the bottom right corner.

The PLAY arrow sometimes needs to be clicked TWICE.

THE VIDEO ABOVE SHOWS HOW TO BUILD
AN EXPRESSION like 2x-3
starting with the x

This Video show how to UNDO the process
so we can ISOLATE the X
to SOLVE an EQUATION

If you Click on an image
a LARGER view will appear.

A general discussion of 

No SOLUTION vs. All REAL NUMBERS 

(This has similar results with = EQUATIONS)

Here is a More Difficult Inequality 

where the VARIABLES completely disappear

 when we try to get them onto one side of < or > or even =

**************STOP HERE***************

The problems below are MORE DIFFICULT.

Your class may never do this level of problem.