olve: $$ x-8 \geq-3 $$ iraph the solutions.

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UpStudy AI · Accepted Answer

Sure, let's solve the inequality $$ x - 8 \geq -3 $$ and graph the solution on a number line.

### **Step 1: Solve the Inequality**

Given:
$$ x - 8 \geq -3 $$

**Add 8 to both sides** to isolate $$ x $$:
$$
x - 8 + 8 \geq -3 + 8 \
x \geq 5
$$

### **Solution:**
$$ x \geq 5 $$

This means that $$ x $$ can be any number **5 or greater**.

### **Step 2: Graph the Solution on a Number Line**

Here's how you can represent the solution on a number line:

```
----|=====>----
    5
```

**Explanation:**

1. **Closed Circle at 5:** 
   - The closed circle (●) at point 5 indicates that 5 is included in the solution ($$ \geq $$ means "greater than or equal to").
   
2. **Arrow to the Right:**
   - The arrow pointing to the right (→) shows that all numbers greater than 5 are included in the solution.

### **Detailed Number Line Representation**

```
<---|----------|----------|----------|--->
    3          4          5          6
                   ●========>
```

- **Number 5:** Marked with a closed circle (●) to show it's included.
- **Arrow (========>):** Extends to the right of 5, indicating all numbers greater than 5 are part of the solution.

### **Alternative Description:**

- **Closed Circle at 5:** Indicates that 5 is a solution ($$ x = 5 $$ satisfies the inequality).
- **Shading to the Right:** Represents all numbers greater than 5.

### **Summary:**

- **Solution:** $$ x \geq 5 $$
- **Graph:** Number line with a closed circle at 5 and shading extending to the right.

If you need a visual diagram, here's a simple text-based illustration:

```
Number Line:  --|----|----●=====>--
               4    5           6
```

- **● (Closed Circle)** at 5 signifies $$ x = 5 $$ is included.
- **=====>** indicates all numbers greater than 5 are part of the solution.
The solution to the inequality $$ x - 8 \geq -3 $$ is $$ x \geq 5 $$. On a number line, this is represented by a closed circle at 5 and an arrow extending to the right, indicating all numbers greater than or equal to 5 are included.

olve: \( x-8 \geq-3 \) iraph the solutions.

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