Question

N.5 Graph solutions to one-step inequalities
TMX
Solve the inequality and graph the solution.
a
3
<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.

Answer 1

To solve the inequality \( 3 < 2 \), we first realize that the statement itself is not correct – \( 3 \) is not less than \( 2 \). However, if there is a misunderstanding and you meant a different inequality, such as \( x + 3 < 2 \), we can go through that example instead.

### Example: Solve the Inequality \( x + 3 < 2 \)

1. **Isolate \( x \)**:
\[
x + 3 < 2
\]
Subtract \( 3 \) from both sides:
\[
x < 2 - 3
\]
\[
x < -1
\]

2. **Graph the Solution**:
- The solution to \( x < -1 \) means that \( x \) can be any number less than \(-1\).
- To graph this inequality:
- Plot the point at \(-1\).
- Since this is a strict inequality (less than, not less than or equal to), we draw an **open circle** at \(-1\).
- Draw a **ray** extending to the left (towards negative infinity) from the open circle at \(-1\).

### Graphic Representation:
- On a number line:
- Place an open circle on \(-1\).
- Draw an arrow to the left from that point.

This indicates that all values left of \(-1\) are included in the solution set while \(-1\) itself is not included.

If you were asking about a different inequality, please let me know!