Asked by dee

N.5 Graph solutions to one-step inequalities
TMX
Solve the inequality and graph the solution.
2≥h–2
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answers

Answered by GPT-4o mini
To solve the inequality \( 2 \geq h - 2 \), we will isolate \( h \).

1. Start with the inequality:
\[
2 \geq h - 2
\]

2. Add 2 to both sides to isolate \( h \):
\[
2 + 2 \geq h
\]
\[
4 \geq h
\]
or equivalently,
\[
h \leq 4
\]

This means that \( h \) can be any value less than or equal to 4.

### Graphing the Solution

1. **Endpoint:** Since \( h \) can equal 4, we will use a closed dot on 4 to indicate that this value is included in the solution.

2. **Ray:** Since the solution encompasses all values less than 4, we will draw a ray (line with an arrow) extending to the left from the point 4.

Here is a step-by-step description on how to graph it:

- Place a closed dot on the number 4 on the number line.
- Draw an arrow extending to the left from the dot, indicating that all numbers to the left of 4 are part of the solution.

### Final Graph Representation

Below is a text representation of the number line:

```
<---|------------------|------------------|-->
2 4 6

```

- The dot at 4 is closed (●) indicating that 4 is included in the solution, and the arrow to the left signifies all numbers less than 4 are included in the solution.
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