To find the value of [tex]\(\frac{x}{3}\)[/tex] given the equation [tex]\(\frac{x+3}{3} = \frac{y+2}{2}\)[/tex], let's go through the steps carefully:
1. Start with the given equation:
[tex]\[
\frac{x+3}{3} = \frac{y+2}{2}
\][/tex]
2. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[
2 \cdot (x + 3) = 3 \cdot (y + 2)
\][/tex]
3. Distribute the constants on both sides:
[tex]\[
2x + 6 = 3y + 6
\][/tex]
4. Subtract 6 from both sides to simplify the equation:
[tex]\[
2x = 3y
\][/tex]
5. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{3y}{2}
\][/tex]
6. Now, substitute this expression into [tex]\(\frac{x}{3}\)[/tex]:
[tex]\[
\frac{x}{3} = \frac{\frac{3y}{2}}{3}
\][/tex]
7. Simplify the fraction:
[tex]\[
\frac{\frac{3y}{2}}{3} = \frac{3y}{2 \cdot 3} = \frac{y}{2}
\][/tex]
Hence, the value of [tex]\(\frac{x}{3}\)[/tex] is:
[tex]\[
\boxed{\frac{y}{2}}
\][/tex]
