We want to graph the following inequality system
[tex]\begin{gathered} x+8\ge9 \\ \text{and} \\ \frac{x}{7}\le1 \end{gathered}[/tex]
First, we need to solve both inequalities. To solve the first one, we subtract 8 from both sides
[tex]\begin{gathered} x+8-8\ge9-8 \\ x\ge1 \end{gathered}[/tex]
To solve the second one, we multiply both sides by 7.
[tex]\begin{gathered} 7\cdot\frac{x}{7}\le1\cdot7 \\ x\le7 \end{gathered}[/tex]
Now, our system is
[tex]\begin{gathered} x\ge1 \\ \text{and} \\ x\le7 \end{gathered}[/tex]
We can combine those inequalities into one.
[tex]1\le x\le7[/tex]
The number x is inside the interval between 1 and 7. Graphically, this is the region between those numbers(including them).
