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Day 5 : Finding the unknown variable value with the Balance MethodDescription: Continuation of basic balancing focusing on the idea of UNDOING what has been done.
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Objective: The purpose of this exercise is to practice the balance method which involves assuming two expressions are in balance and then keeping them in balance until the correct value of the unknown 'variable' becomes obvious. The focus on this exercise is that the Opposite of subtracting is adding and the opposite of multiplying is division.
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08.007 Equations.Mult and Subtraction

Evaluate a where :
     2a - 9 = 3

 

In this question we are told that    2 times some number less 9 gives the result 3

We might guess that the answer is 6 because we see that 2 times 6 (is 12) less 9 gives the result 3

 

However, for more difficult questions we solve this using the balance method

The balance method means that => Whatever we do to the left hand side  we do the same to the right hand side.

On the left hand side we have  2 times by 'a'  - 9.

If we knew what 'a' was, we would multiply it by 2 first and THEN subtract 9.

 

To UNDO that with the balance method, we would FIRST add 9 and THEN divide by 2  ( The reverse of what we would do if we knew the value 'a').

 

  2a - 9 = 3

ADD 9 to both sides  (UNDO subtracting 9)

  2a  = 12

Divide both sides by 2   (UNDO multiplying by 2)

  a = 6

Check your answer.

   2 x 6 - 9  = 3

Correct.

And that's it.