Question

solve for j and graph the solution
-11<_16j+7-7j<16
plot the endpoints

Answer 1

To solve the inequality \(-11 \leq 16j + 7 - 7j < 16\), we first simplify it. The expression \(16j + 7 - 7j\) can be simplified as follows:

\[
16j - 7j + 7 = 9j + 7
\]

Now, the inequality becomes:

\[
-11 \leq 9j + 7 < 16
\]

We can break this into two parts and solve them separately.

### Part 1: Solve \(-11 \leq 9j + 7\)

1. Subtract 7 from both sides:

\[
-11 - 7 \leq 9j
\]

\[
-18 \leq 9j
\]

2. Divide by 9:

\[
-\frac{18}{9} \leq j
\]

\[
-2 \leq j \quad \text{or} \quad j \geq -2
\]

### Part 2: Solve \(9j + 7 < 16\)

1. Subtract 7 from both sides:

\[
9j < 16 - 7
\]

\[
9j < 9
\]

2. Divide by 9:

\[
j < 1
\]

### Combine Both Parts

From the two parts, we found:

\[
-2 \leq j < 1
\]

This means that the solution to the inequality is:

\[
[-2, 1)
\]

### Graph the Solution

To graph the solution on a number line, we'll plot the endpoints:

- A filled circle on \(-2\) indicates that \(-2\) is included in the solution.
- An open circle on \(1\) indicates that \(1\) is not included in the solution.

Here’s how the graph looks:

```
<----●==================○---->
-2 1
```

In summary, the solution to the inequality is \([-2, 1)\), and it is graphed above.