



Sometimes
we have equations that don't use an equal sign (=).



They use
one of 4 other squiggles. 


The
contestants are: 





# 1 





This
means "greater than". 


It means
the stuff on the left side of the equation 


has a
greater value than the stuff on the right side. 


Another
way to think of inequalities, is that in all of these problems 


the
inequality arrow always points towards the stuff with less
value. 


As in: 








# 2 





This
puppy means "less than". 


It means
that the stuff on the left side of the equation 


has a
lesser value than the stuff on the right side. 


As in: 








# 3 





This one
means "greater than OR equal to". 


It is a
combination of ">"
and "=". 


It means
that the stuff on the left side 


either
has a greater value or is of equal value 


than the
stuff on the right side. 


As in: 








# 4 





The last
of our musketeers. 


This one
means "less than OR equal to". 


It is a
combination of "<"
and "=". 


It means
that the stuff on the left side 


either
has a lesser value or is of equal value 


than the
stuff on the right side. 


As in: 








When you
get an equation with one of these things in it, 


it makes
NO DIFFERENCE in how you work the problem. 


Just use
the same two rules in the same way. 





There is
ONE EXTRA DETAIL 


that you
need in some of these problems. 





If you
multiply or divide both sides by a negative number, 


you
reverse the direction that the inequality arrow points. 





OK, now
we're ready to try some problems! 





Example: 


5X  3 > 2 





First you
add 3 to both sides ... 











Now
divide both sides by 5 


to get
the X all by itself. 











And
simplify ... 


X > 1 





OK, now
in this next example, 


we will
need that "reverse the direction" trick. 





Solve
this for X ... 








First
peel the "+ 1" away from the X. 











Now
divide by 3 and watch the inequalities 


change
direction ... 











copyright 2005 Bruce Kirkpatrick 
