Question

Solve for j and graph the solution.
–
11≤16j+7–7j<16 open circle or closed

Answer 1

To solve the compound inequality \(-11 \leq 16j + 7 - 7j < 16\), we can simplify and break it down into two parts.

1. **Solve the left inequality:**
\[
-11 \leq 16j + 7 - 7j
\]
Simplifying the expression in the middle:
\[
-11 \leq 9j + 7
\]
Now, subtract 7 from both sides:
\[
-11 - 7 \leq 9j
\]
\[
-18 \leq 9j
\]
Now, divide both sides by 9:
\[
-2 \leq j \quad \text{or} \quad j \geq -2
\]

2. **Solve the right inequality:**
\[
16j + 7 - 7j < 16
\]
Simplifying the middle expression again:
\[
16j - 7j + 7 < 16
\]
\[
9j + 7 < 16
\]
Subtract 7 from both sides:
\[
9j < 16 - 7
\]
\[
9j < 9
\]
Divide both sides by 9:
\[
j < 1
\]

Putting it together, we have:
\[
-2 \leq j < 1
\]

### Graphing the Solution
To graph this inequality, we will plot it on a number line:
- Mark an open circle at 1 (indicating that 1 is **not** included).
- Mark a closed circle at -2 (indicating that -2 **is** included).
- Shade the region between -2 and 1.

The final graph should look like this:

```
<---(--- ●========●---)--->
-2 1
```

### Summary of the solution:
The solution is \(-2 \leq j < 1\) with a closed circle at -2 and an open circle at 1.