To solve the inequality \( \frac{q}{3} \leq 2 \), we will isolate \( q \).
- Multiply both sides by 3 to eliminate the fraction: \[ q \leq 6 \]
Now we will graph the solution:
- The solution \( q \leq 6 \) means that \( q \) can take any value up to and including 6.
- The endpoint of the inequality is 6.
To plot the solution:
- Plot the point at \( q = 6 \).
- Because the inequality is less than or equal to (\( \leq \)), we will use a closed circle at 6, indicating that it is included in the solution.
- Since the inequality implies all values less than or equal to 6, we shade to the left of 6.
Here is a step-by-step illustration of what you need to do:
- Endpoint: Plot \( 6 \) with a closed circle.
- Direction: Shade to the left to indicate that all values less than or equal to \( 6 \) are included in the solution.
To finalize the graph:
- Select the endpoint \( 6 \) and leave it closed.
- There's no need to delete any part since we are shading to the left, and the interval continues indefinitely in that direction.
The final graph represents all values from \( -\infty \) to \( 6 \), inclusive.