Find the sum of 12a + 7b, −6a − 9, and 14a − 12b.

a) 20a - 5b - 9
b) 20a + 5b - 9
c) 20a - 5b + 9
d) 20a + 5b + 9

The answer is:  [A]:  " 20a − 5b − 9 " .

Explanation:

  (12a + 7b) + (−6a − 9) + (14a − 12b) =
 
   12a + 7b  +  1(−6a − 9) + 1(14a − 12b) =
    
   12a + 7b + (1*-6a) + (1*-9) + (1*14a) + (1* -12b) =
      
    12a + 7b − 6a − 9 + 14a − 12b =  ?

Combine the "like terms:

12a − 6a  + 14a = 20a ; 

7b − 12b =  - 5b ;

and then we have "-9" ;

So, write as:   " 20a − 5b − 9 " ;  which is:  Answer choice:  [A].

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