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Day 3 : Balance method with Negative Variable partDescription: Finding the unknown variable when the co-efficient of the variable is negative
Objective: The purpose of this exercise is to be able to find the unknown value of the variable by dividing by the co-efficient of the variable even when it is negative. As usual you always check your answer to make sure that it works with the original expressions.
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08.011 Equations.On both sides (Sub2)

Evaluate a where :
     8 - 8a = -13 - 5a

To solve this equation we use the balance method as usual.

The only difference is that if you multiply or divide by a negative number be careful to get the right answer.

 

8 - 8a = -13  - 5a

8 - 8 -8a = -13 - 8 -5a 

 -8a = -21 - 5a

-8a +5a = -21 -5a + 5a 

-3a = -21

At this point we have negative 3 times by a is equal to negative 21.

To UNDO the -3 times by 'a'  we divide by the co-efficient of 'a' as usual.

So divide both sides by negative 3

-3a / -3   =  -21 / -3

  a = +7  (Rember that when you are multiplying or dividing, if the signs are the same you get a positive answer, otherwise you get a negative answer).

Check you answer in the original equation

8 - 8a = -13  - 5a

8 - 8 (+7) = -13 -5 (+7)

8 - 56 = -13 - 35

-48 = -48

So using the value +7 for our variable 'a', our two expressions have the same value (-48) as expected.

So answer is 'a' = +7