Given:
The given inequalities are:
[tex]3x+1>7\text{ and 4x}\leq24[/tex]
Solving first inequality, we get:
[tex]\begin{gathered} 3x+1>7 \\ 3x>7-1 \\ 3x>6 \\ x>\frac{6}{3} \\ x>2 \end{gathered}[/tex]
Solving the second inequality, we get:
[tex]\begin{gathered} 4x\leq24 \\ x\leq\frac{24}{4} \\ x\leq6 \end{gathered}[/tex]
Merging the solutions of both inequalities, we get:
[tex]\begin{gathered} x>2\text{ and x}\leq6 \\ \Rightarrow x\epsilon\text{ (2,6\rbrack} \end{gathered}[/tex]
So, the graph will be a number line with an open circle at 2 and a closed circle on 6 and shading in between.
Therefore,
Option A is correct.
