To solve the equation [tex]\( K = 4a + 9ab \)[/tex] for [tex]\( a \)[/tex], let's proceed with the following steps:
1. Rearrange the given equation:
The original equation is
[tex]\[
K = 4a + 9ab
\][/tex]
2. Factor out [tex]\( a \)[/tex]:
Notice that both terms on the right-hand side contain [tex]\( a \)[/tex]. Factor [tex]\( a \)[/tex] out from these terms:
[tex]\[
K = a(4 + 9b)
\][/tex]
3. Isolate [tex]\( a \)[/tex]:
To solve for [tex]\( a \)[/tex], divide both sides of the equation by [tex]\( (4 + 9b) \)[/tex]:
[tex]\[
a = \frac{K}{4 + 9b}
\][/tex]
Thus, the solution for [tex]\( a \)[/tex] in terms of [tex]\( K \)[/tex] and [tex]\( b \)[/tex] is:
[tex]\[
a = \frac{K}{4 + 9b}
\][/tex]
