algebra_Balance_scale

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					        Algebra-Balance Scale
Solve simple linear equations using a balance beam
representation.




               R.Gallinagh September 2005
      Algebra-Balance Scale
.

       3x + 3 = x + 7




    What does x=?




           R.Gallinagh September 2005
                Algebra-Balance Scale
        .

                 3x + 3 = x + 7




What do we need to do to make it balance?




                      R.Gallinagh September 2005
          Algebra-Balance Scale
.

           3x + 3 = x + 7




    We need to put x +7 on other side. Now it is balance




                 R.Gallinagh September 2005
             Algebra-Balance Scale
     .

              3x + 3 = x + 7
What happens if we move a number 1 from left hand side




 No longer balanced……… 3x + 2 does NOT equal x + 7

What do we need to do to make it balance?




                   R.Gallinagh September 2005
             Algebra-Balance Scale
     .

              3x + 2 = x + 6




We need to move 1 from the other side

We have balance again since 3x + 2 does EQUAL x + 6



                   R.Gallinagh September 2005
            Algebra-Balance Scale
    .

             3x + 2 = x + 6




Who took 1 away from the right hand side?
3x + 2 obviously does NOT equal x + 5
What must we do to get BALANCE?


                  R.Gallinagh September 2005
           Algebra-Balance Scale
  .

            3x + 1 = x + 5




YES You are right; we must take away one from the right
hand side
Does 3 x + 1 = x + 5 ……………..Yes it does



                 R.Gallinagh September 2005
              Algebra-Balance Scale
     .

               3x + 1 = x + 5
 Some one has taken 1 away from the right hand side




Does 3x = x + 5 ….The beam tells us it does not.
What do we do for balance?



                    R.Gallinagh September 2005
          Algebra-Balance Scale
  .

           3x = x + 4
  Take 1 away from the right hand side.




           It means   3x = x + 4
We don’t have numbers on both sides; but we do have x’s



                R.Gallinagh September 2005
           Algebra-Balance Scale
.

            3x = x + 4




    Taking x just from one side caused imbalance
    We must take x from other side



                 R.Gallinagh September 2005
            Algebra-Balance Scale
   .
Now we have balance with 2x on one side and 4 on the other side


                    2x = 4




That means x = 2 ………….wow easy


                   R.Gallinagh September 2005
Algebra-Balance Scale

3x + 3 = x + 7




    R.Gallinagh September 2005
    Algebra-Balance Scale

   3x + 3 = x + 7
3x + 3 - 3 = x + 7 - 3




       R.Gallinagh September 2005
    Algebra-Balance Scale

   3x + 3 = x + 7
3x + 3 - 3 = x + 7 - 3
       3x = x + 4




       R.Gallinagh September 2005
    Algebra-Balance Scale

   3x + 3 = x + 7
3x + 3 - 3 = x + 7 - 3
       3x = x + 4
     3x -x = x - x + 4



       R.Gallinagh September 2005
    Algebra-Balance Scale

   3x + 3 = x + 7
3x + 3 - 3 = x + 7 - 3
       3x = x + 4
     3x -x = x - x + 4
        2x = 4


       R.Gallinagh September 2005
    Algebra-Balance Scale

   3x + 3 = x + 7
3x + 3 - 3 = x + 7 - 3
       3x = x + 4
     3x -x = x - x + 4
        2x = 4
         X=2
       R.Gallinagh September 2005

				
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