Graph the inequality below on the number line. $$ x

Question

Graph the inequality below on the number line. $$ x<4 $$

UpStudy AI · Accepted Answer

To graph the inequality $$ x < 4 $$ on a number line, follow these steps:

1. **Draw a Horizontal Line:**
   - This line represents all possible real numbers.

2. **Mark the Number 4:**
   - Place a point at 4 on the number line.

3. **Use an Open Circle at 4:**
   - Since the inequality is "less than" (and not "less than or equal to"), use an open circle around 4 to show that 4 is **not** included in the solution.

4. **Shade to the Left of 4:**
   - Shade all numbers to the left of 4 to indicate that all those numbers are solutions to the inequality $$ x < 4 $$.

### Visual Representation

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

```
<---|----|----|----◦----|----|----|--->
    1    2    3    4    5    6    7
```

- **◦ at 4:** Represents an open circle at 4 (not included).
- **Arrow pointing left:** Indicates that all numbers less than 4 are included in the solution.

### Explanation

- **Open Circle:** The open circle at 4 signifies that 4 itself is **not** a solution to the inequality $$ x < 4 $$.
- **Shading to the Left:** This shading shows that all numbers **less than** 4 satisfy the inequality.

### Example Solutions

Some example values that satisfy $$ x < 4 $$ include:
- $$ x = 3 $$
- $$ x = 0 $$
- $$ x = -2 $$
- $$ x = \frac{7}{2} $$ (which is 3.5)

**Note:** Any number less than 4 is a valid solution, but 4 itself is not included.

### Graphing Tips

- **Closed Circle (●):** Use this when the inequality includes the number (e.g., $$ x \leq 4 $$).
- **Open Circle (◦):** Use this when the inequality does **not** include the number (e.g., $$ x < 4 $$).

By following these steps, you can accurately graph the inequality $$ x < 4 $$ on a number line.
To graph $$ x < 4 $$ on a number line: 1. Draw a horizontal line. 2. Place an open circle at 4. 3. Shade all numbers to the left of 4. This shows that all numbers less than 4 are solutions.

Graph the inequality below on the number line. \( x<4 \)

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