6. Construct Arguments Haley solves the inequality $$ -13 \geq r+7 $$ and graphs the solution on a number line with a solid circle at -20 and an arrow pointing left. is she correct? Support your answer, and give the correct description if she is incorrect.

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UpStudy AI · Accepted Answer

Yes, Haley is **correct** in both solving the inequality and graphing the solution on the number line. Here's a detailed explanation to support this conclusion:

### **Solving the Inequality**

Given the inequality:
$$
-13 \geq r + 7
$$

**Step 1: Isolate $$ r $$**
$$
-13 \geq r + 7
$$

Subtract 7 from both sides to solve for $$ r $$:
$$
-13 - 7 \geq r \quad \Rightarrow \quad -20 \geq r
$$
$$
\Rightarrow \quad r \leq -20
$$

### **Interpreting the Solution**

The solution $$ r \leq -20 $$ means that $$ r $$ can be any real number **less than or equal to -20**.

### **Graphing on the Number Line**

To graph $$ r \leq -20 $$ on a number line:

1. **Solid Circle at -20**: 
   - A **solid (filled) circle** is used at -20 to indicate that -20 is included in the solution set (i.e., $$ r = -20 $$ is a valid solution).

2. **Arrow Pointing Left**:
   - An **arrow pointing to the left** from -20 signifies that all numbers **less than -20** are included in the solution.

Here's a visual representation:

```
<----●=====================
    -20
```

- **●** represents the solid circle at -20.
- **<----** indicates the arrow pointing to the left, covering all numbers less than -20.

### **Conclusion**

Haley correctly:

- **Solved the Inequality**: She accurately determined that $$ r \leq -20 $$.
- **Graphed the Solution**: She appropriately used a solid circle at -20 and an arrow pointing left to represent all values of $$ r $$ that satisfy the inequality.

Therefore, her solution and graph are both **correct**.
Haley is correct. She solved the inequality $$ -13 \geq r + 7 $$ to find $$ r \leq -20 $$ and graphed it with a solid circle at -20 and an arrow pointing left on the number line, accurately representing all values of $$ r $$ that satisfy the inequality.

6. Construct Arguments Haley solves the inequality \( -13 \geq r+7 \) and graphs the solution on a number line with a solid circle at -20 and an arrow pointing left. is she correct? Support your answer, and give the correct description if she is incorrect.

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