Solve for x*x* and graph the solution on the number line below.

4, x, is greater than or equal to, 16

4*x*≥

16

To solve the inequality \(4x \geq 16\), follow these steps:

### Step 1: Solve the inequality
1. **Divide both sides by 4**:
   \[
   \frac{4x}{4} \geq \frac{16}{4}
   \]
2. **Simplify**:
   \[
   x \geq 4
   \]

So, the solution is \(x \geq 4\).

### Step 2: Graph the solution on the number line
- On the number line, mark the point \(4\).
- Since \(x \geq 4\), you will draw a closed circle at \(4\) (indicating that \(4\) is included in the solution).
- Shade the region to the right of \(4\) to represent all values greater than or equal to \(4\).

Here’s how it would look:

```
<---|---|---|---|---|---|---|---|---|---|---|--->
   0   1   2   3   4   5   6   7   8   9  10
                     ●--------------------->
```
The closed circle at \(4\) and the arrow to the right indicate that the solution includes all numbers greater than or equal to \(4\).

Would you like further details or have any questions?

### Related Questions:
1. How would you solve and graph \(5x \leq 25\)?
2. What is the difference between an open circle and a closed circle on a number line?
3. How do you solve and graph the inequality \(2x < 10\)?
4. What happens if the inequality is \(4x \geq -8\) instead?
5. How do you handle compound inequalities like \(2x \leq 6\) and \(3x > 9\)?

**Tip:** When graphing inequalities, use a closed circle for \(\geq\) or \(\leq\) and an open circle for \(>\) or \(<\).

Learn how to solve the inequality 4x >= 16 and graph the solution on a number line. This problem covers key concepts in inequalities and number line graphing, suitable for students in Grades 7-9.

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