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Linear Inequalities (single variable)
This first example will show you how to enter the inequality and how you can enter both sides of the inequality as a way to check the exact location where the inequality begins.

Example 1:    Solve the inequality:     1

  • Enter each side of the inequality into Y1 and Y2

  • Enter the inequality statement into Y3 :   2
    (The inequality symbols are under the TEST Menu - 2nd MATH.)
    This step could also be entered as Y1 < Y2.

  • Graph.  Y3 is horizontal. Use can use the intersect option, (2nd Trace #5 Intersect) on Y1and Y2 to find the "exact" point where the inequality answer begins (which is (-1,-2) and moves left).

  • Do a Boolean Check:  Where the inequality is "true", the y-values on the graph will be a 1. 

  • If you look at the table, 0's will be listed where the inequality is false and 1's will be listed where the inequality is true.  (arrow to the right to see additional tables)

  • Answer:  x < -1

    • Remember that the calculator cannot draw an open or closed circle on the intervals. You will have to determine which circle is needed based upon whether the inequality includes "equal to".

    If you turn off the axes (FORMAT - 2nd ZOOM), you will be able to see the graphing of the 0's and 1's more clearly. 

On older model calculators, notice that the small vertical segment connecting the 0's to the 1's is simply the calculator being set in "connected" mode.  Change to "dot" mode if you want to eliminate this tiny segment. 4



 

 


Graph


Trace, move UP to Y3,
the black spider appears
on the horizontal line.


You can see the break
from Y3 = 1 to Y3 = 0.

Example 2 will show you how the calculator automatically deals with the direction of the inequality.
Example 2:     Solve the inequality:   5
  • Enter the inequality into Y1
     6

  • Graph

  • If you enter the inequality directly into Y1, you will see only the Boolean graph.  It may be necessary to look carefully in your table to find the exact point where the inequality answer begins.

  • Such answers can be found easily if the answers are integer values.  Otherwise, you will want to use the intersect option mentioned in Example 1 to find an "exact" starting point of the inequality.

  • Answer:  x < -2

In this problem, the calculator automatically took care of reversing the direction of the inequality when solving.

The older model graph is shown, with the tiny segment connecting y = 1 to y = 0,  

 

  


7
Example 3 will show you how to deal with a compound inequality, where you must deal with two inequalities at the same time.
Example 3:    Graph the solution set for   2x - 4 < 8   and   x + 5 > 7
 

Algebraic solution:
Solve each equation separately.  The answer
will be points that make BOTH sets true.

7            8

Answer:  2 < x < 6

9

 Graphical solution:
 Both inequalities are entered into Y1 with the use of "and".  
Find "and" by using the CATALOG (2nd 0) or  TEST (2nd MATH)→ LOGIC, #1 and.




Older model.

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