what is the value of t in 13t+15=9t+1

       13t + 15 = 9t + 1

There are two terms on the left, +13t and +15.
There are two terms on the right, +9t and +1

The terms +13t and +9t contain the letter t.
The terms +15 and +1 do not contain the letter t.

The object is:

1. To get rid of all terms on the LEFT which DO NOT contain t.

AND

2. To get rid of all terms on the RIGHT which DO contain t.

So we must get rid of the +15 on the left, and we must get rid 
of the +9t on the right.

To get rid of a term, we add its opposite to both sides.

First we get rid of the +15 on the left.  It's opposite is -15,
so put -15 under the +15 on the left and -15 under the +1, and 
draw a line:

       13t + 15 = 9t + 1
            -15      -15
      -------------------

Now we add vertically. We bring down the 13t, and since the +15
and the -15 cancel out to zero we don't write anything below them.
Then we bring down the = sign, and the +9t.  Then we combine the
+1 and the -15 getting -14:

       13t + 15 = 9t + 1
            -15      -15
      --------------------
       13t      = 9t - 14 

Now we get rid of the +9t on the right.  It's opposite is -9t,
so put -9t under the +13t on the left and -9t under the +9t on
the right, and draw a line:

       13t + 15 = 9t + 1
            -15      -15
      --------------------
       13t      = 9t - 14 
       -9t       -9t
      --------------------
 
Now we combine the 13t and the -9t getting +4t. We bring down
the = sign.  The +9t and the -9t cancel and give zero, so we
don't put anything under them. Then we bring down the +14

             13t + 15 = 9t + 1
            -15      -15
      --------------------
       13t      = 9t - 14 
       -9t       -9t
      --------------------
        4t      =     -14

Next we need to get rid of the 4 coefficient of t.  To get rid
of a coefficient, we divide both sides by the coefficient 4.

             13t + 15 = 9t + 1
            -15      -15
      --------------------
       13t      = 9t - 14 
       -9t       -9t
      --------------------
        4t      =     -14

        4t            -14
       ————    =     ————— 
         4             4

                      -14
          t    =     —————
                       4

We reduce the fraction on the right and
place the negative sign in front of the
fraction:

                      7
          t    =   - ———
                      2

Edwin