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. **Isolate the term with \(n\)** by subtracting 3 from both sides:
\[
-6n + 3 - 3 \geq 21 - 3
\]
\[
-6n \geq 18
\]

2. **Divide both sides by -6**. Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign:
\[
n \leq \frac{18}{-6}
\]
\[
n \leq -3
\]

So, the solution to the inequality is:
\[
n \leq -3
\]

### Graphing the Solution

To graph the solution \(n \leq -3\):

1. **Draw a number line**.
2. **Locate the point -3** on the number line.
3. **Use a closed dot** at -3 to indicate that -3 is included in the solution (since it's a "less than or equal to" inequality).
4. **Shade to the left** of -3 to indicate all numbers less than -3 are included in the solution.

### Description of the Graph

- The graph has a closed dot at -3, indicating that -3 is part of the solution.
- The shaded region extends to the left, representing all values of \(n\) that are less than or equal to -3.