Question

You found that -15 is the boundary point and is also a solution to the inequality. How can you represent this on a number line?
j + 7 ≥ -8

j + 7 = -8
j = -15

-18
-17
-16
-15
-14
-13
-12

-18
-17
-16
-15
-14
-13
-12

Answer 1

To represent the solution to the inequality \( j + 7 \geq -8 \) on a number line, we first need to identify the solution we derived, which is \( j = -15 \).

1. **Identify the boundary point**: You have found that the boundary point is -15. Since the inequality includes "greater than or equal to" (≥), -15 is included in the solution set.

2. **Draw the number line**: You should represent the numbers mentioned (-18 to -12) on the number line.

3. **Mark the boundary point**: Place a closed circle at -15 to indicate that -15 is included in the solution set (because it is a solution to the inequality).

4. **Shade the appropriate area**: Since the inequality is \( j + 7 \geq -8 \) (which translates to \( j \geq -15 \)), you would shade the line to the right of -15 to indicate that all numbers greater than -15 are part of the solution.

### Here’s how your number line should look:

```
-18 -17 -16 -15 -14 -13 -12
<========)
```

- The `)` indicates that -15 is included (closed circle).
- The arrows or shading to the right indicate that all values greater than -15 are also solutions.

Thus, the solution set is \( j \geq -15 \).