Question

solve for the variable c in this equation:
$3a(b + c) = d$
$\bigcirc \\ c = \frac{d + 3ab}{3a}$
$\bigcirc \\ c = \frac{d + 3b}{3a}$
$\bigcirc \\ c = \frac{d - 3ab}{3a}$
$\bigcirc \\ c = \frac{d - 3b}{3a}$

Explanation:

Step1: Divide both sides by \(3a\)

To isolate the term \((b + c)\), we divide both sides of the equation \(3a(b + c)=d\) by \(3a\) (assuming \(a
eq0\)). This gives us \(\frac{3a(b + c)}{3a}=\frac{d}{3a}\), which simplifies to \(b + c=\frac{d}{3a}\).

Step2: Subtract \(b\) from both sides

Next, we subtract \(b\) from both sides of the equation \(b + c=\frac{d}{3a}\) to solve for \(c\). So, \(b + c - b=\frac{d}{3a}-b\). Simplifying the left side gives \(c=\frac{d}{3a}-b\). To combine these terms over a common denominator, we rewrite \(b\) as \(\frac{3ab}{3a}\), so \(c=\frac{d - 3ab}{3a}\).

Answer:

\(c=\frac{d - 3ab}{3a}\) (corresponding to the option \(c=\frac{d-3ab}{3a}\))