Question

literal equations
solve the equation for a.
$k = 4a + 9ab$
options:
$a = 4(k + 9b)$
$a = \frac{4 + 9b}{k}$
$a = k(4 + 9b)$
$a = \frac{k}{4 + 9b}$

Explanation:

Step1: Factor out \(a\) from the right side

Given the equation \(K = 4a+9ab\), we can factor out \(a\) from the terms \(4a\) and \(9ab\) on the right - hand side. Using the distributive property \(ac + bc=(a + b)c\) (in reverse), we get \(K=a(4 + 9b)\).

Step2: Solve for \(a\)

To isolate \(a\), we divide both sides of the equation \(K=a(4 + 9b)\) by \((4 + 9b)\) (assuming \(4+9b
eq0\)). So, \(a=\frac{K}{4 + 9b}\).

Answer:

\(a=\frac{K}{4 + 9b}\) (the option corresponding to this is the one with \(a=\frac{K}{4 + 9b}\))