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

Algebra.Com
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)   (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
:
*********************
a + b = 3 + 4 = 7
*********************
:
Answer by Edwin McCravy(20060)   (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
RELATED QUESTIONS

if f(x)= 3x^2, what are all real values of a and b for which the graph of g(x)= ax^2+b os (answered by stanbon,MathLover1)
If x^2+6x+16=(x+a)^2+b for all values of x. Find a and... (answered by jim_thompson5910)
Let f(x) = 2x + 3. Find values for a and b such that the equation f(ax + b) = x is true... (answered by rothauserc)
A(x-2)^2 + B(x-2) +C ≡ 3x^2 -13x + 19 What are the values of the constants A, B... (answered by Edwin McCravy)
if f(x)=x2+5 then f (a=b)... (answered by longjonsilver)
If x=2a-b^2, then a... (answered by stanbon)
Find the values of X and Y in a b c d a b equals 2y + 1 B C equals y + 1 C D equals 7x-3... (answered by ikleyn,ankor@dixie-net.com,greenestamps)
if x^2+6x+16=(x+a)^2+b for all values of x, find the values of a and... (answered by jim_thompson5910)
if x^2+6x+16=(x+a)^2+b for all values of x, find the values of a and... (answered by jim_thompson5910)