Question 39343
<pre><font size = 5><b>SOLVE THE INEQUALITY. COLLECT
THE XS ON THE LEFT SIDE. WRITE THE SOLUTION SET IN 
INTERVAL NOTATION:

(4/3)(X + 1) < (1/2)(X - 3)

First clear of fractions by multiplying through by 
the LCD of 6:

Start by placing brackets around each side:

     <font color = "red">[</font>(4/3)(X + 1)<font color = "red">]</font> < <font color = "red">[</font>(1/2)(X - 3)<font color = "red">]</font>

Put "6·" in front of each 

   6·<font color = "red">[</font>(4/3)(X + 1)<font color = "red">]</font> < 6·<font color = "red">[</font>(1/2)(X - 3)<font color = "red">]</font>

Use the associative law to switch the brackets:

   <font color = "red">[</font>6·(4/3)<font color = "red">]</font>(X + 1) < <font color = "red">[</font>6·(1/2)<font color = "red">]</font>(X - 3)

          <font color = "red">[</font>8<font color = "red">]</font>(X + 1) < <font color = "red">[</font>3<font color = "red">]</font>(X - 3)

             8X + 8 < 3X - 9

                 5X < -17

                  X < -17/5

Note: in that last step we DO NOT reverse the sign of
inequality because we divided through by a positive
number.

Now we graph the inequality on a number line:

-oo   <==================)-----------------  oo
                      -17/5

Interval notation  (-oo, -17/5)

Edwin
AnlytcPhil@aol.com</pre>