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 \(-6n + 3 \geq 21\), we will follow these steps:

1. **Isolate the term with \(n\)**:
\[
-6n + 3 \geq 21
\]
Subtract 3 from both sides:
\[
-6n \geq 21 - 3
\]
Simplifying the right side gives:
\[
-6n \geq 18
\]

2. **Divide by \(-6\)**:
When dividing both sides of an inequality by a negative number, the direction of the inequality sign changes:
\[
n \leq \frac{18}{-6}
\]
This simplifies to:
\[
n \leq -3
\]

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

### Graphing the Solution

To graph \(n \leq -3\) on a number line:

- Draw a number line.
- Locate the point \(-3\) on the line.
- Place a closed circle (or dot) on \(-3\) to indicate that \(-3\) is included in the solution (since it is "less than or equal to").
- Shade the line to the left of \(-3\) to indicate that all numbers less than \(-3\) are included in the solution.

### Description of the Graph

- The graph contains a closed circle at \(-3\).
- It shades to the left, extending to negative infinity.
- This represents all values of \(n\) that are less than or equal to \(-3\).

In conclusion, the graph visually represents the inequality by indicating the set of all \(n\) values that satisfy \(n \leq -3\).