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Solve the equation for [tex]\( a \)[/tex].

[tex]\[ K = 4a + 9ab \][/tex]

A. [tex]\( a = \frac{K}{4 + 9b} \)[/tex]
B. [tex]\( a = K(4 + 9b) \)[/tex]
C. [tex]\( a = 4(K + 9b) \)[/tex]
D. [tex]\( a = \frac{4 + 9b}{K} \)[/tex]

Sagot :

GinnyAnswer
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]
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