https://file.aiquickdraw.com/mathbot/file/1728507388684guow5vau.jpg

To graph the inequality \( x \leq 3 \), we need to follow these steps:

### Step-by-Step Instructions:

1. **Draw the Boundary Line:**
   - The inequality \( x \leq 3 \) involves the vertical line at \( x = 3 \). 
   - Since the inequality includes \( \leq \) (less than or equal to), the boundary line should be **solid** because points on the line satisfy the inequality.

2. **Plot Points on the Boundary:**
   - Identify points on the line where \( x = 3 \). Examples of such points are \( (3, 0) \), \( (3, 2) \), and \( (3, -2) \).

3. **Shade the Region:**
   - The inequality \( x \leq 3 \) means all values of \( x \) that are less than or equal to 3.
   - Shade the region to the **left** of the vertical line at \( x = 3 \) because that represents the values where \( x \) is less than or equal to 3.

### Summary:
- **Solid vertical line** at \( x = 3 \).
- **Shade the region to the left** of this line.

Would you like more details on this process or have any further questions?

---

Here are 5 related questions to expand this understanding:
1. What happens if the inequality was \( x < 3 \) instead of \( x \leq 3 \)?
2. How would you graph the inequality \( y \geq 2x + 1 \)?
3. How can you determine whether to use a solid or dashed line for inequalities?
4. What changes if the inequality involves both \( x \) and \( y \), like \( y \leq 2x - 5 \)?
5. How do you handle graphing inequalities with horizontal lines, like \( y > 4 \)?

**Tip:** Always remember that a solid line means the boundary points are included (e.g., \( \leq \) or \( \geq \)), while a dashed line means they are not (e.g., \( < \) or \( > \)).

Learn how to graph the inequality x ≤ 3 with step-by-step instructions. This guide explains how to draw the boundary line, plot points, and shade the region on a coordinate plane. Suitable for middle school students, Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation