5x - 4 is greater than or equal to 2x + 11. graph the solution.

To graph the solution of the inequality \( 5x - 4 \geq 2x + 11 \), we follow these steps:

### Step 1: Solve the Inequality
We already solved the inequality and found:
\[ x \geq 5 \]

### Step 2: Graphing on a Number Line
1. **Draw a number line:** Start by drawing a horizontal line and marking relevant points, especially \( x = 5 \).

2. **Plot the solution \( x \geq 5 \):**
   - **Closed circle at \( x = 5 \)**: Since the inequality is \( \geq \), we include \( x = 5 \) in the solution, so place a solid (closed) circle on the number line at \( x = 5 \).
   - **Shade the region to the right of 5**: The inequality \( x \geq 5 \) means that all values greater than or equal to 5 satisfy the inequality. So, shade the line to the right of the point \( x = 5 \) to indicate all these values.

Here's what the graph should look like:

- The number line will have a solid circle at 5, with a shaded line extending to the right, indicating that the solution includes all numbers greater than or equal to 5.

---

Would you like further details or have any questions?

Here are 5 related questions:

1. How would the graph change if the inequality were \( x > 5 \) instead of \( x \geq 5 \)?
2. Can you describe what the graph would look like for \( x \leq 5 \)?
3. How do you graph inequalities on a coordinate plane?
4. What happens if we have a compound inequality like \( 3 \leq x < 7 \)?
5. What is the importance of the type of circle (open or closed) in inequality graphs?

**Tip:** Always double-check if the circle should be open or closed based on whether the inequality includes the value ( \( \geq \) or \( \leq \) for closed circles, \( > \) or \( < \) for open circles).

Learn how to graph the solution of the inequality 5x - 4 >= 2x + 11 step-by-step with detailed instructions. This problem involves inequalities and graphing on a number line, essential concepts for algebra students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation