Solve the inequality and graph the solution.

Question

q
3
≤2
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 \( \frac{q}{3} \leq 2 \), we will isolate \( q \).

1. 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:

1. Plot the point at \( q = 6 \).
2. 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.
3. 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.