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.(2 points)

Answer 1

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

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

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

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

### Graphing the Solution:

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

- Draw a number line.
- Locate the point -3 on the number line.
- Since \(n\) can be equal to -3, draw a closed (or filled) circle at -3.
- Shade to the left of -3 to indicate that all values less than -3 are included in the solution.

### Description of the Graph:

The graph has a closed circle at -3 (indicating that -3 is included in the solution), and the shading extends to the left, representing all numbers less than -3. The graph visually shows that the solution encompasses all values down to negative infinity.