Question

make a line graph represents the solutions to this inequality: 5n−3<3(n+1)

Answer 1

To create a line graph representing the solutions to the inequality \( 5n - 3 < 3(n + 1) \), we first need to solve the inequality step by step.

1. **Distribute on the right side:**
\[
5n - 3 < 3n + 3
\]

2. **Rearrange the inequality to isolate \( n \):**
- Subtract \( 3n \) from both sides:
\[
5n - 3n - 3 < 3
\]
- Simplifying this gives:
\[
2n - 3 < 3
\]

3. **Add 3 to both sides:**
\[
2n < 6
\]

4. **Divide both sides by 2:**
\[
n < 3
\]

Now, we have determined that the solution to the inequality is \( n < 3 \).

### Line Graph Representation

To represent this solution graphically:

- Draw a horizontal line (number line).
- Mark the number \( 3 \) on this line.
- Use an open circle at \( 3 \) to indicate that \( 3 \) is not included in the solution set.
- Shade the line to the left of \( 3 \), indicating all values less than \( 3 \) are solutions.

### ASCII Representation

Here's a simple ASCII representation of the line graph:

```
<-----|-----|-----|-----|-----|-----|----->
0 1 2 3 4 5
o
<--------- (n < 3)
```

**Key:**
- The open circle at "3" denotes that \( n = 3 \) is not part of the solution set.
- The shaded line to the left of "3" represents all values less than \( 3 \).