To find an expression equivalent to [tex]\( a \)[/tex] given the equation [tex]\(\frac{4a}{b} = 12\)[/tex], let's solve this step-by-step:
1. Step 1: Start with the given equation.
[tex]\[
\frac{4a}{b} = 12
\][/tex]
2. Step 2: Isolate [tex]\( a \)[/tex].
To isolate [tex]\( a \)[/tex], we first need to get rid of the fraction by multiplying both sides of the equation by [tex]\( b \)[/tex]:
[tex]\[
4a = 12b
\][/tex]
3. Step 3: Solve for [tex]\( a \)[/tex].
Next, we divide both sides of the equation by 4 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{12b}{4}
\][/tex]
4. Step 4: Simplify the expression.
Simplify the right-hand side of the equation:
[tex]\[
a = 3b
\][/tex]
So, the expression equivalent to [tex]\( a \)[/tex] is [tex]\( 3b \)[/tex].
Thus, the correct answer is:
(B) [tex]\( 3b \)[/tex]
