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Geometry of Equations

Review question

What is the largest $x$ to satisfy these three inequalities?
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Ref: R9709

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Question

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

\(6\),
\(7\),
\(8\),
\(9\).