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# Writing and Graphing One-Variable Inequalities

## Writing and Graphing One-Variable Inequalities 1.2 - Solution

a
First, we see that the circle at the endpoint is open. This indicates that $x=\text{-}4$ is not included in the interval.

Next, we observe that the graph is to the right of the endpoint. Using $x$ to represent the graph, we can express the inequality as $x$ is greater than $\text{-}4.$ Algebraically, it can be written as $\begin{gathered} x > \text{-}4. \end{gathered}$

b
The circle is closed which means that the endpoint should be included.

The graph is to the right of the endpoint, so it represents all values greater than or equal to $x=2.$ Thus, our inequality can be written with the $\geq$ symbol as $\begin{gathered} x\geq2. \end{gathered}$

c
To write an inequality for the given graph, we need to take note of the endpoint and the direction of the inequality.

First, we see that the circle at the endpoint is open. This means that $2$ is not included. Next, we observe that the graph lies to the left of the endpoint. Therefore, the inequality should be written as $x$ less than $2.$ $\begin{gathered} x < 2 \end{gathered}$