Given the equation:
[tex]\[
\frac{x + 3}{3} = \frac{y + 2}{2}
\][/tex]
we want to find the expression for [tex]\(\frac{x}{3}\)[/tex].
First, we start by cross-multiplying to eliminate the fractions:
[tex]\[
2 \cdot (x + 3) = 3 \cdot (y + 2)
\][/tex]
This simplifies to:
[tex]\[
2x + 6 = 3y + 6
\][/tex]
Next, we subtract 6 from both sides of the equation:
[tex]\[
2x = 3y
\][/tex]
Now, we solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{3y}{2}
\][/tex]
Finally, we need to find [tex]\(\frac{x}{3}\)[/tex]. Substituting [tex]\(x\)[/tex] into the expression gives:
[tex]\[
\frac{x}{3} = \frac{\frac{3y}{2}}{3}
\][/tex]
This simplifies by multiplying both the numerator and the denominator:
[tex]\[
\frac{x}{3} = \frac{3y}{2 \cdot 3} = \frac{y}{2}
\][/tex]
Thus, the value of [tex]\(\frac{x}{3}\)[/tex] is:
[tex]\[
\frac{x}{3} = \frac{y}{2}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\frac{y}{2}}
\][/tex]
