SOLUTION: If a(x+b)=3x+12 for all values of x, then a+b equals to what?

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Question 1071822: If a(x+b)=3x+12 for all values of x, then a+b equals to what?
Found 2 solutions by rothauserc, Edwin McCravy:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
a(x+b) = 3x+12
:
ax +ab = 3x + 12
:
a = 3, then 3b = 12 and b = 4
:
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a + b = 3 + 4 = 7
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:

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

a(x+b)=3x+12

Since that is to be true for all values of x,
it's true when x = 0.  So,

a(0+b)=3(0)+12
  a(b)=0+12
    ab=12

It's also true when a=1, so

a(1+b)=3(1)+12
  a+ab=3+12
  a+ab=15, and since ab=12,
  a+12=15
     a=3

And since ab=12
          3b=12
           b=4

So a(x+b)=3x+12  is really just
   3(x+4)=3x+12

An application of the distributive principle.

Edwin