Question

Solve and graph the solution to the inequality −6n+3≥21 on your own paper or device. In the box below, give the solution to the inequality and describe how your graph looks.

Answer 1

To solve the inequality \(-6n + 3 \geq 21\), follow these steps:

1. **Subtract 3 from both sides:**
\[
-6n \geq 21 - 3
\]
\[
-6n \geq 18
\]

2. **Divide both sides by -6:**
When dividing or multiplying both sides of an inequality by a negative number, remember to flip the inequality sign.
\[
n \leq \frac{18}{-6}
\]
\[
n \leq -3
\]

The solution to the inequality is \(n \leq -3\).

### Graph Description
On a number line, the graph of the solution will look like this:

- Draw a horizontal line representing the number line.
- Place a closed dot (or solid dot) at \(-3\) to indicate that \(-3\) is included in the solution (since the inequality is less than or equal to).
- Shade the area to the left of \(-3\) to show all numbers less than \(-3\) are included in the solution.

Overall, the graph represents all real numbers less than or equal to \(-3\).