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=-8j=-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 solve the inequality:

1. Rewrite the inequality:
\[
j + 7 \geq -8
\]

2. Subtract 7 from both sides:
\[
j \geq -8 - 7
\]
\[
j \geq -15
\]

Now, we know that \( -15 \) is the boundary point for the inequality, and it is included in the solution since the inequality is "greater than or equal to" (≥).

### To represent this on a number line:

1. **Draw a horizontal line**.

2. **Mark the relevant points**:
- Place a point at \( -15 \).
- Draw arrows or labels that mark values less than and greater than \( -15 \).

3. **Indicate the boundary point**:
- Since \( -15 \) is included in the solution (due to the "≥" sign), represent it with a **closed circle** at \( -15 \).

4. **Shade to the right**:
- Shade the number line starting from \( -15 \) and extending rightwards to show that all values greater than \( -15 \) are included in the solution.

### Example of how it looks on a number line:
```
<---|---|---|---|---|---|---|---|---|---|---|--->
-18 -17 -16 [ -15 ) -14 -13 -12 ...
↑ shaded to the right
```

Where:
- The closed bracket `[ -15 )` indicates that \(-15\) is included in the solution set (the dot is filled in).
- The shading to the right shows that all numbers greater than \(-15\) are also part of the solution.