1 Answer

Charles Cavalcante · Answer 1 · 2023-09-24T01:11:35+0000

We want to graph the following inequality system

$\begin{gathered} x+8\ge9 \\ \text{and} \\ (x)/(7)\le1 \end{gathered}$

First, we need to solve both inequalities. To solve the first one, we subtract 8 from both sides

$\begin{gathered} x+8-8\ge9-8 \\ x\ge1 \end{gathered}$

To solve the second one, we multiply both sides by 7.

$\begin{gathered} 7\cdot(x)/(7)\le1\cdot7 \\ x\le7 \end{gathered}$

Now, our system is

$\begin{gathered} x\ge1 \\ \text{and} \\ x\le7 \end{gathered}$

We can combine those inequalities into one.

$1\le x\le7$

The number x is inside the interval between 1 and 7. Graphically, this is the region between those numbers(including them).

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