Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Writing and Graphing One-Variable Inequalities

Writing and Graphing One-Variable Inequalities 1.2 - Solution

arrow_back Return to Writing and Graphing One-Variable Inequalities
a
First, we see that the circle at the endpoint is open. This indicates that x=-4x=\text{-}4 is not included in the interval.

Next, we observe that the graph is to the right of the endpoint. Using xx to represent the graph, we can express the inequality as xx is greater than -4.\text{-}4. Algebraically, it can be written as x>-4.\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.x=2. Thus, our inequality can be written with the \geq symbol as x2.\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 22 is not included. Next, we observe that the graph lies to the left of the endpoint. Therefore, the inequality should be written as xx less than 2.2. x<2\begin{gathered} x < 2 \end{gathered}