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Day 4 : Finding the unknown variable value with the Balance MethodDescription: Basic two step balancing of equal expressions.
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Objective: The purpose of this exercise is to practice the balance method which does exactly the same thing to both expressions until a solution is obvious. This exercise requires two steps. The first is addition or subtraction to both sides, the second is division of both sides.
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08.006 Equations.Mult and Addition

Evaluate a where :
     5a + 9 = 39

In this question we are told that    5 times some number plus 9 gives the result 39

Clearly the answer is 6 because   5 times six plus 9 gives the result 39.

 

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  5 times by 'a'  + 9.

If we knew what 'a' was, we would multiply it by 5 first and THEN add 9.

 

To UNDO that with the balance method, we would FIRST subtract 9 and THEN divide by 5  ( The reverse of what we would do if we knew the value 'a').

 

  5a +  9   = 39

Subtract 9 from both sides  (UNDO adding 9)

  5a  = 30

Divide both sides by 5   (UNDO multiplying by 5)

  a = 6

Check your answer.

   5 x 6 +9  = 39

Correct.

And that's it.