Solve the inequality and graph the solution.

Question

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).