The numbers \(x\) and \(y\) satisfy the following inequalities
\[\begin{align*}
2x+3y &\le 23, \\
x+2 &\le 3y, \\
3y+1 &\le 4x.
\end{align*}\]

The largest possible value of \(x\) is

\(6\),

\(7\),

\(8\),

\(9\).

Can we draw a diagram? Where are all the inequalities satisfied?

Or would working purely algebraically be more useful?

Where in this region does the largest value of \(x\) occur?