Question 223968

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