Question 223968: My son's homework question is:
Find the value(s) of a for which the equation is an identity.
a(2x+3) = 9x + 12 - x
What exactly are they asking him to do here? I don't understand what they are looking for. Should he solve for a, or for x in terms of a?
thanks,
Andrea
Found 3 solutions by nerdybill, scott8148, MathTherapy:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website!
Find the value(s) of a for which the equation is an identity.
a(2x+3) = 9x + 12 - x
.
The problem wants to know the value of 'a'.
Start by distributing the 'a' to the terms inside the parenthesis:
2ax+3a = 9x + 12 - x
Combine like-terms on the right:
2ax+3a = 8x + 12
Looking at the 'x' terms:
(2a)x+3a = (8)x + 12
To get the SAME number of x's on the left as the right, the following MUST be true:
2a = 8
a = 4
.
Similarly:
3a = 12
a = 4
.
Therefore, a=4
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! an identity means that the two sides of the equation are not ony equal, but also identical
3x = 12 is an equation ___ there is a unique value of x (solution)
3x = 3x is an identity ___ all values of x will work (no solution)
solving for "a" will generate the identity
collecting terms ___ a(2x+3) = 8x + 12
factoring ___ a(2x+3) = 4(2x + 3)
dividing by 2x+3 ___ a = 4
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website! My son's homework question is:
Find the value(s) of a for which the equation is an identity.
a(2x+3) = 9x + 12 - x
What exactly are they asking him to do here? I don't understand what they are looking for. Should he solve for a, or for x in terms of a?
thanks,
Andrea
a(2x + 3) = 9x + 12 - x
a(2x + 3) = 9x - x + 12
a(2x + 3) = 8x + 12
a(2x + 3) = 4(2x + 3)
As seen, there is a common factor on each side of equation, and that common factor is 2x + 3
As can be seen also, "a" MUST equal 4.
If this is still unclear, let's consider the following:
b(2 + 1) = 5(2 + 1). We're supposed to get "b" = 5.
Let's go the long way.
b(2 + 1) = 5(2 + 1)
2b + b = 5(3)
3b = 15
Therefore, as stated previously, 
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