To this instance in this chapter we've concentrated on solving out equations.  Now it is time to switch gears a little & begin thinking regarding solving inequalities.  Before we get into solving inequalities we have to go over a couple of the basics first.

It is assumed that you know that

                                                         a < b

refer that a is any number which is strictly less that b. It is also supposed that you know that

                                                         a ≥ b

means that a is any number that is either strictly bigger than b or is exactly equivalent to b.  Alike it is supposed that you know how to deal along with the remaining two inequalities. > (greater than) and ≤ (less than or equal to).

What we desire to discuss is some notational facts and some subtleties which sometimes get students while the really start working with inequalities.

First, recall that while we say that a is less than b we refer that a is to the left of b on a number line.  Thus,

                                                      -1000 > 0

is a true inequality.

After that, don't forget how to appropriately interpret ≤ and ≥ .  Both of the following are true inequalities.

                                    4 ≤ 4                                                   -6 ≤ 4

In the primary case 4 is equivalent to 4 and thus it is "less than or equal" to 4.  In the second case -6 is strictly less than 4 & so it is "less than or equal" to 4. The most common fault is to select that the first inequality is not a true inequality.  Also be careful to not take this interpretation & translate it to < and/or >.  For instance,

                                                  4 < 4

is not a true inequality as 4 is equivalent to 4 and not less than 4.

At last, we will be seeing several double inequalities .