Question
\begin{tabular}{l|l} Write the inequality in \\ interval notation and \\ graph. \\ \( x \geq-1 \)\end{tabular}
Ask by Hammond Schultz. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The inequality \( x \geq -1 \) is written in interval notation as \([-1, \infty)\). On the number line, it's represented by a closed circle at \(-1\) and shading to the right.
Solution
**Step 1. Express the inequality in interval notation.**
The inequality is given by
\[
x \geq -1.
\]
This means that all numbers \( x \) that are greater than or equal to \(-1\) are included. In interval notation, this is written as:
\[
[-1, \infty).
\]
**Step 2. Graphing the inequality on a number line.**
1. Draw a horizontal number line.
2. Place a closed (filled) circle at \(-1\) to indicate that \(-1\) is included in the solution.
3. Shade or draw an arrow extending to the right of \(-1\) to represent all numbers greater than \(-1\).
A simple representation of the graph is shown below:
\[
\text{Number line:} \quad \underset{(-\infty)}{\longleftarrow} \quad \; \bullet_{-1} \,\,\text{==========> } \,\, (\infty)
\]
Here, the filled circle at \(-1\) indicates that \(-1\) is included, and the arrow to the right represents all \( x \geq -1 \).
**Final Answer:**
- **Interval Notation:** \([ -1, \infty )\)
- **Graph:** A number line with a closed circle at \(-1\) and shaded to the right.
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Beyond the Answer
For the inequality \( x \geq -1 \), the interval notation is \( [-1, \infty) \). This means that the solution includes the value -1 and all values greater than -1. To graph this inequality, start by drawing a number line. Place a closed circle on -1 to indicate that -1 is included in the solution. Then, shade the line to the right of -1 to represent all the numbers greater than -1, extending infinitely.