Question 38553
<pre><font size = 5><pre><b>Solve the inequality symbolically. Express the solution set in interval
notation.

        7y - 2 < -6y - 7

Solve it just as you would an equation
Get rid of the -2 on the left by adding +2 to both sides

        7y - 2 < -6y - 7 
           + 2       + 2
       ——————————————————
        7y     < -6y - 5

Get rid of the -6y on the right by adding +6y to both sides

            7y < -6y - 5
           +6y   +6y
          ———————————————
           13y <      -5

Divide both sides by 13.  Note: if you were dividing by a 
negative number, you would reverse the inequality symbol;
however here we are dividing by a positive number 13, so
we DO NOT reverse the inequality symbol:

           13y < -5
             y < -5/13 

Now draw a number line, and mark -5/13 approximately
which is between -1 and 0, closer to 0

       --------------o-----------
        -2     -1      0      1 

Since y is less than -5/13, shade the left side of -5/13

      <==============o-----------
        -2     -1      0      1

We imagine that there is a -<font face = "symbol">¥</font> on the far
left of the number line and an <font face = "symbol">¥</font> on the
far right side

 -<font face = "symbol">¥</font>   <==============o-----------    <font face = "symbol">¥</font>
        -2     -1      0      1
 
The left "endpoint" of the shaded region is -<font face = "symbol">¥</font> and the
right endpoint is -5/13, so the interval notation has these
two endpoints.  Neither endpoint is included, so the interval
notation has ( ) of each side, not [ ]:

Interval notation of solution:    (-<font face = "symbol">¥</font>,-5/13)

Edwin McCravy
AnlytcPhil@aol.com</pre>