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:

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

Put "6·" in front of each 

   6·[(4/3)(X + 1)] < 6·[(1/2)(X - 3)]

Use the associative law to switch the brackets:

   [6·(4/3)](X + 1) < [6·(1/2)](X - 3)

          [8](X + 1) < [3](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