Question

Solve the inequality and graph the solution.
1≤
q+6
3
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( 1 \leq \frac{q + 6}{3} \), we start by eliminating the fraction by multiplying both sides by 3:

\[
3 \cdot 1 \leq q + 6
\]

Which simplifies to:

\[
3 \leq q + 6
\]

Next, we isolate \( q \) by subtracting 6 from both sides:

\[
3 - 6 \leq q
\]

This simplifies to:

\[
-3 \leq q
\]

or, equivalently,

\[
q \geq -3
\]

The solution to the inequality is \( q \geq -3 \).

### Graphing the solution:

1. **Endpoints**: The endpoint of the solution is \( -3 \).
2. **Closed/Open endpoint**: Since the inequality is \( \geq \), we use a closed dot at \( -3 \) to indicate that this point is included in the solution.
3. **Direction**: The inequality shows that \( q \) is greater than or equal to \( -3 \), which means we shade to the right of \( -3 \).

### Final graph representation:

- Mark a closed dot at \( -3 \).
- Shade the region to the right of \( -3 \) (indicating all values \( q \) greater than \( -3 \)).

In summary, the solution and its graph consist of a closed dot at \( -3 \) and a shaded region extending to the right (indicating all values from \( -3 \) to positive infinity).